United States

Department of

Agriculture

Forest Service

Southern 

Research Station

Research Paper

SRS–37

An Outdoor Recreation Use Model 

with Applications to Evaluating 

Survey Estimators

Stanley J. Zarnoch, Donald B.K. English, and 

Susan M. Kocis
The Authors

September 2005

Southern Research Station

P.O. Box 2680

Asheville, NC 28802

Stanley J. Zarnoch, Mathematical Statistician, USDA Forest Service, Southern 

Research Station, Asheville, NC 28802; Donald B.K. English, Visitor Use 

Monitoring Program Manager, USDA Forest Service, WO–RHR, Washington, DC 

20250-1125; and Susan M. Kocis, Visitor Use Assistant Program Manager, USDA 

Forest Service, WO–RHR, East Lansing, MI 48823.

Cover photo: Arkansas Buffalo National River in the Ozark Mountains.

Photo by: Bill Lea.
i

An Outdoor Recreation Use Model 

with Applications to Evaluating

Survey Estimators

Stanley J. Zarnoch, Donald B.K. English, 

and Susan M. Kocis
ii
iii

Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

The National Visitor Use Monitoring Sampling Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Model Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

 Types of Site Visitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

 Arriving and Last-Exiting Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

 Number of Intermediate Exits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

 Time of Intermediate Exits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

 Trap Shyness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

 Parameterization of ORUS to the NVUM Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

 Simple Simulation Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

 Estimator Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
iv
1

An Outdoor Recreation Use Model with

Applications to Evaluating Survey Estimators

Stanley J. Zarnoch, Donald B.K. English, and Susan M. Kocis

Abstract

An outdoor recreation use simulator (ORUS) has been developed to simulate recreation survey data currently being obtained by the U.S. Department 

of Agriculture Forest Service, National Visitor Use Monitoring (NVUM) 

program’s survey of the national forests of the United States. Statistical 

distributions represent the various behaviors of recreationists during their 

visit to a recreation site. The beta distribution is used to model arriving 

times and last-exiting times. The Poisson distribution is used to model the 

number of intermediate exits from the site, and the times of the exits are 

selected randomly according to the uniform distribution. Finally, three 

levels of trap shyness are assigned to the recreationists to quantify the probability that the recreationists will be captured by the interviewer. The beta 

distributions for arriving and last-exiting are parameterized to the NVUM 

survey data. The functioning of the simulator is demonstrated with a simple 

example. The utility of ORUS in evaluating the bias and coefficient of 

variation of various survey scenario estimators of recreation use is also 

presented.

Keywords: Last-exiting recreationist, National Visitor Use Monitoring, 

ORUS, simulation, trap shy.

Introduction

Outdoor recreation has recently become a very important

commodity of forests and in many situations it is given higher

priority than more traditional forest products. Dependable, 

accurate estimates of recreation use are increasingly critical 

in national, regional, and local forest-level decisionmaking 

and planning. They are necessary in assessing recreation 

benefits from forests and for quantifying the impacts on 

other forest resources and local economies.

Although forest inventories have been developed for estimating the traditional timber values of forests, until recently 

no large scale, statistically based analog has existed for 

estimating recreation use. However, in 1996 a pilot study 

was initiated to develop a field survey for estimating recreation use on the national forests throughout the United 

States (Zarnoch and others 2002). This was modified and 

expanded substantially to also include characteristics of the 

visitors, their satisfaction with the recreation resource, and 

their economic impact on the local community (English and 

others 2002). This has led to the U.S. Department of Agriculture Forest Service (Forest Service), National Visitor Use 

Monitoring (NVUM) program, which has now completed 

a full multiyear cycle of sampling all national forests in the 

United States. While the NVUM survey was designed for 

use on the national forests of the United States, the basic 

methodology is under study by several other Federal and 

State agencies in the United States that need quality estimates of visitation on recreation lands on which recreation 

sites are usually dispersed. 

One step in the review process of the first NVUM survey 

cycle is that a critical evaluation of the visitation estimators 

be performed to determine their potential bias and variance 

properties and to evaluate methodological changes that can 

reduce one or the other. To that end, an outdoor recreation 

use simulator (ORUS) has been developed that can provide 

data similar to that collected across the national forests 

during the first NVUM survey cycle. 

The simulator benefits efforts to estimate recreation use 

on forest lands in several ways. First, the model outlines a 

structure that allows researchers to decompose the complex 

system of visitor behavior into a set of more easily understood components and to demonstrate how these components are related to the recreation use estimator. Second, 

the model provides a process that makes possible detailed 

analysis of the statistical properties of the recreation use 

estimator. Third, the model enables a researcher to isolate 

and describe the effects of different assumptions about one 

or more visitor behaviors on the properties of the recreation 

use estimator. Finally, the model can provide guidance on 

the effects of scheduling alternatives for the amount and 

timing of on-site interviewing on both the quality of the 

recreation use estimate and the volume of visitor characteristic data collected. 

The specific objectives of this paper are to (1) describe a 

simulation model (ORUS) for outdoor recreation use estimation, (2) parameterize ORUS to the first NVUM survey 

cycle data, (3) illustrate the functioning of ORUS with a 

simple example, and (4) demonstrate the evaluation of the 

recreation use estimator under various theoretical scenarios.
2

The National Visitor Use Monitoring

Sampling Design

The NVUM program performs surveys that collect data 

about visitors on the U.S. national forests. The survey 

employs a stratified multistage sampling design based on 

rotating panels that are spread over a 5-year sampling cycle. 

All national forests in the United States are sampled once 

every 5 years, with approximately one-fifth of the forests 

in each of nine regions sampled each year. This statistical 

methodology follows conventional sample survey techniques 

(Cochran 1977) with a few modifications to incorporate 

specific situations inherent in sampling of national forests 

for recreation use.

The NVUM sampling design divides each national forest 

into areas that are called site types, each of which contains a 

multitude of individual sites exhibiting similar recreational 

attributes. Four mutually exclusive site types served as 

stratification variables for reducing variation in the survey’s 

estimates. These sites types are:

• Day-use developed sites (DUDS)—sites intended for 

day use only, including boating areas, picnic sites, fishviewing sites, fishing sites, information sites, interpretive 

sites, observation sites, playground-park sport sites, ski 

areas (alpine and Nordic), wildlife viewing areas, visitor 

centers, museums, swimming areas, and winter sports 

areas; generally, DUDS provide visitor comfort, convenience, and educational opportunities, but they are available only on a day-use basis

• Overnight-use developed sites (OUDS)—include campgrounds, cabins, hotels, lodges, resorts, horse camps, 

organization sites, and any other overnight facility on 

national forest lands, whether they are owned or managed 

by the Forest Service or are private concessions

• Wilderness sites (WILD)—sites that are designated official wilderness areas

• General forest area (GFA)—all national forest sites that 

are not designated as DUDS, OUDS, or WILD

Since recreationists’ behavior could vary by site type and 

thus exert differential effects on the recreation use estimates, 

the simulation model was developed to exhibit the unique 

behavior associated with each of these four site types. 

For the first survey cycle, there were approximately 2,700 

DUDS, 5,000 OUDS, 3,200 WILD, and 16,500 GFA individual sites distributed throughout the national forests of 

the United States. DUDS were open for recreation use for 

∼528,000 site days annually, OUDS for ∼668,000 site days 

annually, WILD sites for ∼516,000 site days annually, and 

GFA sites for ∼3,368,000 site days annually.

In the NVUM survey the primary measurement variable is 

the number of recreationists who were completing a visit 

to a given site on a given day. These are termed last-exiting 

recreationists, and this term distinguishes them from recreation visitors who are making intermediate (non-final) exits 

and who will return to the site. An exact value for lastexiting recreationists would be obtained if each site were 

monitored on an around-the-clock basis and if all visitors 

exiting each site were required to participate in an on-site 

interview. Such a protocol is not possible for several obvious 

reasons. Consequently, NVUM uses methods that estimate 

the measurement variable indirectly. A 24-hour mechanical 

count of all traffic is obtained along with 6 hours of vehicle 

occupant interviewing and exiting vehicle counts at a 

designated interview point traversed by visitors exiting the 

site or area of the forest. This process obtains (1) a ratio of 

observed exiting vehicles to the 6-hour mechanical vehicle 

count which is then used to calibrate the 24-hour mechanical 

vehicle count, yielding an estimate of total exiting vehicles 

for the 24-hour period (VEHC); (2) an estimate of the 

proportion of exiting vehicles that carry last-exiting recreationists (PBAR); and (3) the average number of people in 

a last-exiting recreation vehicle (PEOPVEH).1 These three 

values are used to estimate recreation use at the site for 24 

hours.

The NVUM site visit estimator for recreation use is defined 

as

SV = PBAR*VEHC*PEOPVEH (1)

where

SV = the site visit estimator defined as the number of lastexiting recreationists on a given site for the entire 24-hour 

day

PBAR = the proportion of last-exiting recreationists estimated from a 6-hour interview survey

VEHC = the calibrated number of vehicles exiting the site 

for the entire 24-hour day

PEOPVEH = the average number of people in a last-exiting recreation vehicle estimated from the 6-hour interview 

survey

1 A recreation vehicle refers to any type of vehicle that contains recreationists and does not refer only to the typical outdoor recreation vehicle. 
3

It should be noted that SV is based on the number of lastexiting recreationists but that it could have also been based 

on first-entering recreationists. In either case, this eliminates 

multiple counting of recreationists who exit and re-enter the 

site. When site visits are combined over all sampled days, 

an annual estimate of site visits is obtained. For more details 

on this and other aspects of the NVUM methodology, see 

English and others (2002). 

The accuracy of SV depends on how well each of the three 

components in equation (1) is estimated. PEOPVEH is 

obtained by simply counting occupants in last-exiting 

recreation vehicles. Obtaining a sufficient sample size for 

accurate estimation of PEOPVEH is usually not problematic, as the range of values observed is relatively small. 

The accuracy of VEHC depends largely on the consistent 

performance of the mechanical traffic counter over the 24-

hour period and a relatively constant ratio of exiting to total 

traffic. The focus of this paper is on simulating and evaluating the effect of PBAR on SV. PBAR is a complex variable that is highly dependent on several aspects of visitor 

behavior at the recreation site.

Model Components

Types of Site Visitors

The first distinction in types of visitors at a site is between 

those who are there for recreation and those who are there for

some non-recreation purpose (NREC). The latter may include

agency personnel or contractors who are working, and people

who have stopped to use restroom facilities, to obtain information, or for other reasons. Although NREC visitors may be

important in some situations and ORUS is capable of incorporating them into realistic simulations, they are not discussed

further in this paper. The model emphasizes the typical 

outdoor recreationist, and thus recognizes four distinct types 

of recreationists who may be at a site on a given site day. 

The typology is based on their specific behavior patterns of 

arriving time, last-exiting time, and intermediate (non-final) 

exits from the site. These types are defined as follows:

• LERB2 = a recreationist who will be last-exiting the site 

on that site day and was at the site before the official 

beginning of the site day at midnight

• LERD = a recreationist who will be last-exiting the site on 

that site day and arrived on the site during the site day

• NLERB = a recreationist who will not be last-exiting the 

site on that site day and was on the site before the official 

beginning of the site day at midnight

• NLERD = a recreationist who will not be last-exiting the 

site on that site day and arrived on the site during the site 

day

The distinction between LERBs and LERDs deals mainly 

with the amount of time on the site. LERBs are generally on

site longer and are likely to have more intermediate exits. A 

similar distinction is made between NLERBs and NLERDs. 

The four types of recreationists could have similar or different

arriving or last-exiting distribution parameters and intermediate exit rates as will be explained in the next sections.

A DUDS site will usually only have recreationists of the 

LERD type, although it is possible that a few recreationists 

may stay overnight. On the other hand, an OUDS site typically has LERBs, NLERBs, and NLERDs but few LERDs. 

However, the simulator is flexible enough to allow occasional day use in an OUDS if this is specified in the simulation. Other special considerations can be accommodated 

by the simulator. For example, an OUDS may only contain 

LERBs on a Sunday if it is assumed that all campers will 

exit and return home on Sunday night to begin the work 

week on Monday. The GFA and WILD sites may contain 

all four types if both overnight camping and day use are 

possible. In addition, for site days where multiple recreation 

types are permissible, varying proportions of the types may 

be allocated to mimic a realistic situation and the parameters 

that control their individual behavior patterns need not be 

the same. 

Arriving and Last-Exiting Times

The fundamental behavior for recreationists involves 

arriving at the site, engaging in recreation, and then 

exiting the site. The distributions of these actions relative to interview times are key elements of the simulation 

model. Arriving and last-exiting times for recreationists are 

modeled using the beta distribution, which is defined as

(2)

where

a > 0, b > 0, and 0 < p < 1. 

The mean of this distribution is and the variance is

 . The beta distribution takes on a wide

variety of shapes depending on its parameters a and b. For 

2 The acronyms for the types of site visitors are formed by a combination

of (LER or NLER) and (B or D) where LER represents “last-exiting recreationist,” NLER represents “nonlast-exiting recreationist,” B represents 

“before,” and D represents “during.” 
4

instance, the uniform distribution is a special case of the 

beta when a = b = 1 with a mean of 0.50. If a = 1 and b = 5 

then the beta is skewed to the right with a hump in the left 

of the distribution and, consequently, a mean of 0.17. On the 

other hand, if a = 5 and b = 1 then the opposite is true with 

a mean of 0.83. A symmetric bell-shaped distribution with 

a mean of 0.5 occurs when a = b = 5. If a and b are both < 1 

then a u-shaped distribution results. Figure 1 shows the beta 

distribution for several values of the parameters.

The arriving time (AT) of a recreationist is determined by 

selecting a random variate p1 from the specified beta distribution and determining the arriving time as that proportion 

of the recreation day after the start of the recreation day. 

Mathematically, for LERD and NLERD this is

AT = DS

 + p1(DE – DS) (3)

where

DS = time when the recreation day starts3

DE = time when the recreation day ends 

Since LERB and NLERB recreationists are on the site 

previous to the site day, they have no arriving time for that 

site day. Thus, if the recreation day is assumed to be from 

6.00 to 18.00 (6:00 a.m. to 6:00 p.m.) with a uniform distribution of arriving times (a = b = 1) then arrivals occur at 

random throughout the day and the mean arriving time is 

5

4

3

2

1

0

f(p)

a = 0.1 b = 0.1: Dotted line

a = 1.0 b = 1.0: Dashed line

a = 5.0 b = 5.0: Solid line

0 1

p

5

4

3

2

1

0

f(p)

a = 1.0 b = 5.0: Dotted line

a = 5.0 b = 5.0: Solid line

a = 5.0 b = 1.0: Dashed line

0 1

p

5

4

3

2

1

0

f(p)

a = 5.0 b = 2.0: Dotted line

a = 5.0 b = 5.0: Solid line

a = 5.0 b = 8.0: Dashed line

0 1

p

5

4

3

2

1

0

f(p)

a = 2.0 b = 5.0: Dotted line

a = 5.0 b = 5.0: Solid line

a = 8.0 b = 5.0: Dashed line

0 1

p

Figure 1—The beta distribution f(p) for various values of the parameters a and b.

3

 Times used throughout this paper are represented as real numbers for 

computational purposes. The hour component is analogous to standard 

military time while the minute component represents the decimal part of the 

hour. Thus, 6:30 a.m. is represented as 6.50 while 4:15 p.m. is represented 

as 16.25.
5

12.00 (12:00 noon). Obviously, if morning arrivals or afternoon arrivals are more typical, the beta distribution’s parameters could be altered to reflect this situation.

Another variate, p2

, is selected from the beta distribution and 

is used to calculate the last-exiting time of a recreationist. 

For LERBs, last-exiting time is defined as

LET = DS + p2(DE – DS) (4)

and for LERDs as

LET = AT + p2(DE – AT) (5)

Since DS and DE are fixed parameters specified in the simulator depending on the characteristics of the site under 

study, the arriving time variate p1 in equation (3) and the 

last-exiting time variate p2 in equation (4) are selected from 

the beta distribution specified in the simulation for the given 

site. However, for the LERD situation in equation (5), each 

visitor usually has a unique arriving time and it is conceivable that different beta distributions of last-exiting times 

may result for individuals. The simulator allows for the beta 

parameters to be adjusted with a regression model. Since 

NLERB and NLERD recreationists do not exit the site on 

the site day, they have no last-exiting time. Thus, NLERB 

has neither arriving time nor last-exiting time beta distributions.

The mean arriving time, also known as the mathematical 

expectation E, for LERD and NLERD for a given beta 

distribution is easily found from equation (3) as

(6)

The mean last-exiting time for LERB from equation (4) is

(7)

The mean last-exiting time for LERD from equation (5) is a 

little more difficult to obtain. Let 

(8)

Taking first the component on the far right of equation (8) 

and substituting AT from equation (3) we have

(9)

Note that if p1 and p2 are independent betas (which may not 

be a valid assumption in some instances) then

(10)

This implies that 

(11)

Thus, substituting equations (6), (9), and (11) into equation 

(8) we get for LERD 

(12)

Equations (6), (7), and (12) estimate the theoretical mean 

arriving and last-exiting times based on the parameters of 

the appropriate beta distributions.

Number of Intermediate Exits

Some visitors will make intermediate exits from the site before

completing their recreation visit. Intermediate exits are 

defined as an exit and re-entry into the recreation site on the 

same day. Intermediate exits affect the accuracy of the PBAR

estimate through their relation to the probability that an individual will be surveyed and to trap shyness (to be discussed 

later). The number of intermediate exits a recreationist 

performs during the site day is modeled with the Poisson 

distribution which assumes that they occur at random 

throughout the day. The Poisson distribution is defined as

(13)

where 

x = 0,1,2,3,... and λ > 0. 

The mean and variance of the Poisson are both λ. The 

parameter λ represents the intermediate exit rate of a recreationist for the length of an active recreation day, DE – DS

, 

during which it is assumed that such exits are possible. This 

could be assigned to be the total 24-hour day if it is believed 

that intermediate exits occur throughout this time span. However, more realistically, these exits are usually from around 

a little before dawn to somewhat after dusk, which would 

encompass at most 15 hours. The simulator provides for such

flexibility by defining λ as the intermediate exit rate only 

during the assumed active recreation day defined for that 

specific site day. All individuals within a recreationist type 

have the same λ, but this λ is adjusted by the length of stay 
6

for each recreationist at the site. For instance, an NLERD 

entering a site at 6.00 has more time that day for intermediate exits than one that enters at 12.00 because neither will 

complete a visit that day. The rate is adjusted based on the 

proportion of the active recreation day that is available to a 

recreationist. Thus, a recreationist who is there only a third 

of the active recreation day will have the parameter set at 

λ/3 and the number of intermediate exits will be selected 

from a Poisson distribution with this parameter. Specifically, 

for LERBs this is 

(14)

for LERDs this is

(15)

for NLERBs this is

(16)

and for NLERDs this is

(17)

It is important to note that λ controls only intermediate exits 

and does not include exits for the last time. Last exits are 

controlled by the last-exiting beta distribution. It is assumed 

that last exits are a special movement and are dependent on 

the recreationist type. It is possible to assume that the intermediate exit rate is the same for all recreationist types or it 

may vary depending on the parameters chosen for each.

Time of Intermediate Exits

The specific times of intermediate exits are selected at random

from the total length of stay that a recreationist has for the

site day. This appears to be a reasonable assumption because

each recreationist is unique and has intermediate exit behavior

that is nearly impossible to predict. Some may wander off 

the site as soon as they get there merely to see what’s around 

the next bend. Others may go out to the store only to immediately leave again when they find that they forgot to get an 

important item. Still others may never leave the site until they

depart for home. The total length of stay for the site day is

defined by the arriving time and last-exiting time. The number

of intermediate exits is then used to randomly select a time 

for each exit. The uniform distribution is applied to the total 

length of stay for the site day to generate these variates.

Trap Shyness

The estimation of PBAR used for the site visit estimator, 

SV, is based on the assumption that interviewed vehicles 

are selected at random from those passing over the vehicle 

counter. Unfortunately, stopping to be interviewed is 

optional. Forest Service regulations usually prohibit mandatory traffic stops. Thus, some exiting individuals may choose 

not to be interviewed. The probability that a recreationist 

stops for an interview may very well depend on the recreationist’s previous history of being stopped on that site day. 

For instance, the probability that a recreationist stops for 

an initial interview may be 0.9. However, after being interviewed that day on an intermediate exit, the recreationist 

may not be so eager to be interviewed again and the probability may drop to 0.1. This phenomenon is commonly 

known as trap shyness, a term that originated in animal 

studies in which trapped animals learn to avoid traps after 

they are captured once. Thus, trap shyness by the recreationists will change the probability of being interviewed and 

invalidate the random sample needed for an unbiased estimate of PBAR.

Although an infinite number of trap shyness behaviors could 

be modeled, only three will be discussed here. First, the not 

trap-shy situation is defined as

(18)

where 

Pi = probability that a recreationist will stop to be interviewed given i previous interviews on that site day.

In this situation, all probabilities are equal. For a mild 

degree of trap shyness, the probabilities diminish by half 

after the first interview:

(19)

In extreme trap shyness there is zero probability that there 

will be another interview after the first one:

(20)

The opposite situation, trap addiction, may also occur when 

being interviewed is a very good experience to the recreationist. For instance, if a reward of some type is given after 

the interview process, the recreationist may become more 

eager to be interviewed again. Any level of trap shyness or 

addiction can be incorporated into the model.

= . . .

= . . .
7

distributions to the NVUM sampled survey data. Estimators for the a and b parameters of the beta distribution were 

obtained by using the method of moments. This equates to 

simply setting the sample mean, X, and variance, S2, equal 

to the theoretical beta mean and variance, respectively. This 

yields two equations and two unknowns, which are easily 

solved for b and then a, yielding

(25)

and

(26)

Arrival times for recreation visitors were obtained from 

the NVUM survey and beta distributions fitted for LERDs 

and NLERDs for each of the four site types. Similarly, lastexiting times were used to fit beta distributions to LERBs 

and LERDs for the site types.

The beta distribution of last-exiting times for LERD recreationists was presumed to be dependent on the arriving time 

of an individual. Thus, the beta parameters in this situation 

were not estimated based on the sampled X and S2. Instead, 

two linear regression models were used to predict X and S2 

as functions of arriving time. Thus, each individual recreationist with a unique arriving time had a unique predicted X

and S2 which were used in equations (25) and (26) to predict 

the individual’s beta parameters.

Results

Parameterization of ORUS to the NVUM Data

ORUS could be used to evaluate outdoor recreation surveys 

and their estimators under any hypothetical scenario or 

assumed distribution of arriving and last-exiting times. 

However, to illustrate how ORUS could be tailored to fit a 

specific set of recreation sites, the arriving and last-exiting 

beta distributions were parameterized to the complete set of 

NVUM data collected over the first two sampling years. It 

was assumed that on-site recreation could occur from 6.00 

to 21.00 hours, so the beta distributions are based on this 

recreation day length.

Although there are 4 site types, 4 visitor types, and 2 types 

of beta distributions (arriving and last-exiting times), there 

are only 16 beta distributions to parameterize. The LERB 

recreationists have only a distribution of last-exiting times 

for a given survey day. The LERDs have both arriving and 

Methods

The PBAR estimator for the proportion of last-exiting recreationists that exit from a site is defined as

(21)

where

LC11 = number of last-exiting recreationists captured in 

the interview process

LC01 = number of non-last-exiting recreationists that were 

captured

This could be computed from the data produced by the 

ORUS model under a specific scenario. The true proportion 

of last-exiting recreationists could also be computed as

(22)

where

LC10 = number of last-exiting recreationists that were not 

captured

LC00 = number of non-last-exiting recreationists that were 

not captured

Comparison of the estimated PBAR to the true PBAR for 

a given simulation scenario reveals the quality of the site 

visit estimator, SV. However, since comparisons from only 

one simulation are difficult to judge because the simulated 

values are stochastic, 10,000 simulations were performed. 

An estimate of the bias results from averaging the differences for the 10,000 simulations. Thus, the percent bias is 

defined as

(23)

where 

SVi is defined in equation (1) and

(24)

Note that VEHC and PEOPVEH are fixed constants in the 

simulator and cancel out from equation (23).

Although SV could be evaluated under hypothetical beta 

distributions, it is more realistic and useful to fit the beta 
8

last-exiting beta distributions. The NLERBs neither enter 

nor exit during the survey day, so they have no beta distributions to parameterize. Since the NLERDs only enter and do 

not exit, they have only arriving distributions. The parameter 

estimates along with the sample size and mean and variance 

of the distributions are shown in table 1. Distributions for 

the developed site types (DUDS and OUDS) are graphed 

in figure 2 and for dispersed site types (WILD and GFA) in 

figure 3. Generally, the distributions for the DUDS appeared 

to be quite similar to those for OUDS, and distributions for 

WILD resembled those for GFA.

Table 1—Parameter estimates for the beta distributions of arriving and last-exiting times pooled over the NVUM survey 

data from all regions and forests

Visitor type Movement DUDS OUDS WILD GFA

LERB Arriving a = not defined a = not defined a = not defined a = not defined 

b = not defined b = not defined b = not defined b = not defined

LERB Last-exiting a = 3.053 a = 3.557 a = 4.208 a = 3.694

b = 3.488 b = 6.112 b = 4.462 b = 4.150

n = 789 n = 3727 n = 1088 c = 1322

Mean = 0.467 Mean = 0.368 Mean = 0.485 Mean = 0.471 

Variance = 0.033 Variance = 0.022 Variance = 0.026 Variance = 0.028

LERD Arriving a = 2.987 a = 2.581 a = 2.196 a = 1.602

b = 4.119 b = 3.933 b = 4.383 b = 3.422

n = 11365 n = 1264 n = 3302 n = 10822

Mean = 0.420 Mean = 0.396 Mean = 0.334 Mean = 0.319 

Variance = 0.030 Variance = 0.032 Variance = 0.029 Variance = 0.036

LERD Last-exitinga

 a = 0.903 a = 1.077 a = 1.890 a = 2.022

b = 3.514 b = 3.262 b = 3.574 b = 4.402

n = 10701 n = 1184 n = 3220 n = 10822

Mean = 0.204 Mean = 0.249 Mean = 0.346 Mean = 0.313 

Variance = 0.030 Variance = 0.035 Variance = 0.035 Variance = 0.029

NLERB Arriving a = not defined a = not defined a = not defined a = not defined 

b = not defined b = not defined b = not defined b = not defined

NLERB Last-exiting a = not defined a = not defined a = not defined a = not defined 

b = not defined b = not defined b = not defined b = not defined

NLERD Arriving a = 1.840 a = 2.410 a = 1.458 a = 1.520

b = 1.541 b = 1.803 b = 1.859 b = 1.687

n = 364 n = 3618 n = 971 n = 1240

Mean = 0.544 Mean = 0.572 Mean = 0.440 Mean = 0.474 

Variance = 0.057 Variance = 0.047 Variance = 0.057 Variance = 0.059

NLERD Last-exiting a = not defined a = not defined a = not defined a = not defined 

b = not defined b = not defined b = not defined b = not defined

NVUM = National Visitor Use Monitoring; DUDS = day-use developed sites; OUDS = overnight-use developed sites; WILD = wilderness sites; GFA = general 

forest area; LERB = a recreationist who will be last-exiting the site on that site day and was at the site before the official beginning of the site day at midnight; 

LERD = a recreationist who will be last-exiting the site on that site day and arrived on the site during the site day; NLERB = a recreationist who will not be lastexiting the site on that site day and was on the site before the official beginning of the site day at midnight; NLERD = a recreationist who will not be last-exiting 

the site on that site day and arrived on the site during the site day.

aThese parameters require regression models to predict the mean and variance as a quadratic function of the arriving time of a recreationist. The values for the 

LERD last-exiting parameters across the site types in this row are averages because they change depending on the specific arriving times that are simulated.
9

5

4

3

2

1

0

f(p)

DUDS LERB

Last-exiting

0 1

p

5

4

3

2

1

0

f(p)

OUDS LERB

Last-exiting

0 1

p

5

4

3

2

1

0

f(p)

DUDS LERD

Arriving and last-exiting

0 1

p

5

4

3

2

1

0

f(p)

OUDS LERD

Arriving and last-exiting

0 1

p

5

4

3

2

1

0

f(p)

DUDS NLERD

Arriving

0 1

p

5

4

3

2

1

0

f(p)

OUDS NLERD

Arriving

0 1

p

Figure 2—The beta distribution f(p) of arriving and last-exiting times for day-use developed sites (DUDS) and overnight-use developed sites 

(OUDS) where solid lines are arriving distributions and dashed lines are last-exiting distributions; (LERB = a recreationist who will be lastexiting the site on that site day and was at the site before the official beginning of the site day at midnight, LERD = a recreationist who will be 

last-exiting the site on that site day and arrived on the site during the site day, NLERD = a recreationist who will not be last-exiting the site on 

that site day and arrived on the site during the site day).
10

5

4

3

2

1

0

f(p)

WILD LERB

Last-exiting

0 1

p

5

4

3

2

1

0

f(p)

GFA LERB

Last-exiting

0 1

p

5

4

3

2

1

0

f(p)

WILD LERD

Arriving and last-exiting

0 1

p

5

4

3

2

1

0

f(p)

GFA LERD

Arriving and last-exiting

0 1

p

5

4

3

2

1

0

f(p)

WILD NLERD

Arriving

0 1

p

5

4

3

2

1

0

f(p)

GFA NLERD

Arriving

0 1

p

Figure 3—The beta distribution f(p) of arriving and last-exiting times for wilderness sites (WILD) and general forest area sites (GFA) where 

solid lines are arriving distributions and dashed lines are last-exiting distributions; (LERB = a recreationist who will be last-exiting the site on 

that site day and was at the site before the official beginning of the site day at midnight, LERD = a recreationist who will be last-exiting the 

site on that site day and arrived on the site during the site day, NLERD = a recreationist who will not be last-exiting the site on that site day and 

arrived on the site during the site day).
11

The LERB recreationists last exited earliest from the OUDS 

sites, with a mean last-exiting beta variate of 0.368 [11.52 

hours computed with equation (7)] and with a distribution 

slightly skewed to the right. Beta distributions for the other 

site types were more symmetric throughout the day. WILD 

had the largest mean last-exiting beta variate of 0.485 (13.28 

hours) while values for both DUDS with 0.467 (13.00 

hours) and GFA with 0.471 (13.06 hours) were just slightly 

less. Although logically it would appear that LERB recreationists should not be on DUDS sites because overnight use 

is not defined on this site type, there were occasional DUDS 

LERB recreationists in the NVUM database, so this distribution was fitted to accommodate such situations.

LERD recreationists arrived earliest on the GFA sites with a

mean beta variate of 0.319 [10.78 hours computed with equation (6)] and latest on the DUDS with a mean beta variate of

0.420 (12.30 hours). Values for the other site types were intermediate with those for WILD being 0.334 (11.01 hours) and

OUDS being 0.396 (11.94 hours). For all site types, and especially for WILD and GFA, the distributions were skewed to 

the right, indicating a tendency for most of these one-day 

visitors to come early in the day. The last-exiting distributions

show two contrasting relationships. Many DUDS and OUDS 

recreationists tend to depart soon after they arrive, as can be 

seen by their exponential type patterns. In contrast, most of 

the WILD and GFA recreationists do not leave as quickly, 

but tend to exhibit a more symmetric distribution but with a 

strong skew to the right. The mean last-exiting beta variates 

were 0.204 [14.07 hours computed with equation (12)] for 

DUDS, 0.249 (14.20 hours) for OUDS, 0.346 (14.47 hours) 

for WILD, and 0.313 (13.98 hours) for GFA. Thus, the mean 

visit duration is simply the difference between E(LET) and 

E(AT). Performing the calculations reveals that for LERD 

recreationists the visit duration at DUDS was 1.77 hours, 

OUDS was 2.26 hours, WILD was 3.46 hours, and GFA was

3.20 hours. It must be emphasized that these visit durations

are for LERD recreationists who do not spend the night at the

site. Obviously, overnight recreationists such as NLERBs and

NLERDs would have a much longer visit duration. It is interesting that for the developed site types (DUDS and OUDS) a

LERD recreationist (who by definition makes only a day visit)

stays approximately 2 hours while on the dispersed site types

(WILD and GFA) the visit duration is over 3 hours. The additional hour may be due to the more remote access to the dispersed sites or to a desire to achieve a longer, more intense 

outdoor recreation experience or to both of these causes.

The NLERD recreationists at DUDS and OUDS sites arrived

an average of 1.51 hours later than did those at the WILD 

and GFA sites. The DUDS had a mean arriving beta variate 

of 0.544 [14.16 hours computed with equation (6)] and that

for OUDS was 0.572 (14.58 hours) while those for WILD 

and GFA were 0.440 (12.60 hours) and 0.474 (13.11 hours),

respectively. It is interesting that for all site types the NLERD

distributions do not display the skewed, asymmetrical bell 

shape of the LERD distributions.

Simple Simulation Example

A simple example illustrates the ORUS model’s capabilities. 

The assumptions for this scenario site day are:

1. a DUDS site, open from 6.00 until 21.00 hours with 

LERD = 10 recreationists 

2. the interviewer was on site from 8.00 until 14.00 hours

3. the daily rate of intermediate exits was set high at λ = 4

4. arriving times and last-exiting times were selected from 

the beta distributions that were parameterized with the 

NVUM data (table 1)

5. to illustrate the effect of trap shyness, the probability of 

capture on a recreationist’s first exit was set at 1.0 and 

then set at 0.0 for any subsequent exits, including the last

These assumptions imply that an average recreationist on 

site for the total 15-hour active recreation day would make 

four intermediate exits in addition to a last exit. Since most 

do not stay for 15 hours, the observed number of intermediate exits is considerably less.

Results from this scenario site day are shown in table 2. There

were a total of 17 exits from the site during the 15-hour day, 

10 of which were obviously last exiting. Only 2 of the 10 lastexiting recreationists were captured. Seven last exited the site

after the interviewers left at 14.00 hours and thus could not 

be captured. The other one was interviewed first during an 

intermediate exit and trap shyness precluded that individual 

from being interviewed on the final exit from the site. A total

of five recreationists were stopped by the interviewers. Thus, 

an estimate of PBAR from equation (21) is PBAR = 2/5 = 0.40.

The true proportion is PBAR = 10/17 = 0.59 computed from

equation (22). This estimate of PBAR results in poor estimates

for recreation use on this site. Assuming that the vehicle 

counter correctly recorded 17 exiting vehicles for the 24-hour

period and that there was an average of 1 person per vehicle 

(for simplicity), the SV estimate would be SV = 0.40(17)(1) 

= 6.8 while the true SV would be SV = 0.59(17)(1) = 10.0. 

This would represent a negative 32-percent bias.

Although the model has simulated data in accordance with 

the specified probability distributions, it is interesting to 

compare the results to what is expected theoretically. From 

equation (6) the theoretical mean arriving time is calculated as

E(AT) = 6 + (21 – 6)(0.420) = 12.30
12

which compares quite well to the mean arriving time of 

12.52 computed from table 2. Similarly, the theoretical mean 

last-exiting time is calculated from equation (12) as

E(LET) = 6 + (21 – 6)[0.420 + 0.204 – 0.420(0.204)] = 14.07

and from table 2 the mean last-exiting time is 14.30. This 

close agreement between the theoretical and simulated data 

indicates that the simulator is reflecting the properties that 

were designed into it. The slight departure is due merely 

to the simulated sampling error inherent in the statistical 

models. If this example were replicated many times and the 

arriving and last-exiting times computed and averaged, they 

would converge to the theoretical means as the number of 

simulations increased.

Thus, if a survey crew is sampling from 8.00 to 14.00 hours 

as in this site, what are the consequences if their sampling 

stops at or before the mean last-exiting time for the recreationists? In this one simulated example, the data reveal that 

only 3 of the 10 recreationists last exited before the survey 

crew was finished interviewing, one of whom was already 

captured and had become trap shy. Thus there were only 

five interviews, and only two of those interviewed were lastexiting recreationists. Since very few recreationists were 

interviewed, it may be more efficient to perform the survey 

later in the day. 

Although mean number of intermediate exits was set at λ = 4

for this simulation example, no recreationist had four intermediate exits. The largest was for recreationist 10, who had 

Table 2—Simulation of a DUDS site day where the recreation day was from 6.00 to 21.00 hours, the interview period 

was from 8.00 to 14.00 hours, l = 4, and P0 = 1.0 and P1 = 0.0; there were 10 LERD recreationists on this site,

PBAR = 0.59, and PBAR = 0.40

Visitor Arrived Last exit Exited Captured Remarks

1 12.23 Yes 14.44 No Not captured because left after interviewers

2 16.87 Yes 18.37 No Not captured because left after interviewers

3 9.20 Yes 10.17 Yes Captured because P0

 = 1.0

4 14.16 Yes 15.11 No Not captured because left after interviewers

5 9.47 No 9.89 Yes Captured because P0 = 1.0

5 No 12.48 No Not captured because became trap shy

5 Yes 12.60 No Not captured because became trap shy

6 10.88 Yes 10.91 Yes Captured because P0

 = 1.0

7 15.27 Yes 16.43 No Not captured because left after interviewers

8 10.61 No 11.27 Yes Captured because P0 = 1.0

8 No 14.69 No Not captured because left after interviewers and

also became trap shy

8 Yes 15.33 No Not captured because left after interviewers and

also became trap shy

9 14.71 Yes 15.19 No Not captured because left after interviewers

10 11.79 No 12.54 Yes Captured because P0 = 1.0

10 No 12.56 No Not captured because became trap shy

10 No 12.88 No Not captured because became trap shy

10 Yes 14.50 No Not captured because left after interviewers and

also became trap shy

DUDS = day-use developed sites; LERD = a recreationist who will be last-exiting the site on that site day and arrived on the site during the site day.
13

three. The observed number of intermediate exits is reasonable because most visitors were on site far less than the total

15 hours. The mean visit duration is computed as the difference between E(LET) and E(AT), which is 14.07–12.30=1.77,

implying that the average number of intermediate exits is 

calculated from equation (15) as (1.77/15)4=0.47. The data 

from table 2 reveal that there was an average of 0.70 intermediate exits, which is close to the theoretical value of 0.47. 

Estimator Evaluation

An evaluation of the site visit estimator SV under several 

scenarios was performed for DUDS sites. The recreation day 

was set at 6.00 to 21.00 hours with LERD = 10 recreationists and an interview window of 8.00 to 14.00 hours. The 

arriving and last-exiting beta distributions parameterized 

with the NVUM survey data were used. With these as the 

base parameters, evaluations were performed to determine 

the effect of trap shyness, intermediate exit frequency, and 

length of interview period. Each scenario is based on 10,000 

replicated simulations and the results are shown in table 3. 

For simplicity, the results are based on SV assuming that 

PEOPVEH = 1.

Scenarios A and B show the effect of trap shyness with 

a low level of intermediate exits (λ = 1). In scenario A 

Table 3—Results from several scenarios for a DUDS site where the recreation day was 

from 6.00 to 21.00 hours with 10 LERD recreationists

Simulation Interview Percent 

scenario times λ P0

, P1, P2, . . . na SV bias CV

hours

A 8.00 1 1, 1, 1, . . . 9,993 9.70 -3.04 11.9

14.00

B 8.00 1 1, 0 9,990 9.57 -4.30 14.6

14.00

C 8.00 4 1, 1, 1, . . . 9,997 9.13 -8.74 19.6

14.00

D 8.00 4 1, 0 9,997 8.79 -12.07 28.1

14.00

E 6.00 1 1, 1, 1, . . . 359 6.99 -30.11 75.4

8.00

F 6.00 1 1, 1, 1, . . . 4,541 8.84 -11.64 45.4

10.00

G 6.00 1 1, 1, 1, . . . 9,370 9.44 -5.60 25.0

12.00

H 12.00 1 1, 1, 1, . . . 10,000 10.17 1.73 7.4

18.00

I 14.00 1 1, 1, 1, . . . 9,978 10.36 3.59 11.7

18.00

J 16.00 1 1, 1, 1, . . . 8,652 10.59 5.94 17.1

18.00

DUDS = day-use developed sites; LERD = a recreationist who will be last-exiting the site on that site day and 

arrived on the site during the site day.

aAlthough the specified target number of simulations for a given scenario was 10,000, not all simulations gave 

results because some did not capture any recreationists for a given simulation, which resulted in no estimate. Thus, 

n is the number of simulations that were actually performed for a given scenario that gave valid estimates. 
14

there was no trap shyness and in B there was extreme trap 

shyness. Both scenarios yielded estimates of SV that differed 

slightly from the true SV = 10 with A having a percent 

bias of -3.04 and B of -4.30. Here, trap shyness negatively 

affected estimator performance, but only slightly because 

the bias was small. Trap shyness was also examined in 

scenarios C (none) and D (extreme) but with an elevated 

intermediate exit rate (λ = 4). Results showed a percent 

bias of -8.74 for C and -12.07 for D, which illustrates that 

increasing the number of intermediate exits can increase 

the negative bias almost threefold. Thus, increasing the 

number of intermediate exits tends to accent the effect of 

trap shyness.

The effect of interview length on the SV estimator was 

examined under λ = 1 and non-trap-shy scenarios E to J. 

These six scenarios altered interviewer time from the first 

2 hours in the morning to the first 4 and then first 6, and 

then to the last 6 in the afternoon, then last 4 and finally last 

2 before 18.00 hours. The true SV for these situations was 

10. Estimates for the morning were all negatively biased, 

with the earliest 2-hour scenario being the worst at -30.11 

percent. In the afternoon a slight positive bias was observed, 

and this was greatest—only 5.94 percent—in the last-2-hour 

scenario. The general conclusions from these particular 

scenarios are that (1) mornings have a large negative bias 

while afternoons have a small positive bias, (2) longer interview periods are better, and (3) these negative and positive 

biases will probably not balance out if a 50-to-50 mix of 

morning and afternoon interview times is selected.

Evaluation of the bias and coefficient of variation of a prenoon SV estimator (8.00 to 14.00 hours) and a post-noon

SV estimator (12.00 to 18.00 hours) under a range of numbers

of intermediate exits was performed on a DUDS site (fig. 4). 

The site was open from 6.00 to 21.00 hours with LERD = 50

recreationists each with probability of capture of 0.9 for all 

exits. The results indicate that both estimators are unbiased 

when λ = 0. However, as λ increases the pre-noon estimator 

becomes quite negatively biased, approximately 10 percent 

when λ = 5. The post-noon estimator showed the opposite 

effect, but with a positive bias of only about half the magnitude of that for the pre-noon estimator. The coefficient of 

variation of both estimators was < 10 percent, which is 

quite reasonable, with that for the post-noon estimator being 

somewhat smaller and more desirable.

The previous scenario was performed again but for a GFA 

site where there was an equal mixture of 10 visitors from 

each of the 4 recreation types (fig. 5). In this situation, the 

pre-noon estimator was again negatively biased and the 

post-noon estimator positively biased, but bias of the postnoon estimator was much larger. In addition, the coefficient 

of variation was approximately the same. Thus, in this 

scenario, the pre-noon estimator is preferable. This emphasizes the fact that the effect of recreationists’ behavior on the 

SV estimator is complex, that general statements about the 

quality of an estimator cannot be easily extended to other 

scenarios, and that the use of a simulation model such as 

ORUS can help in evaluating alternative estimators. 

12

8

4

0

-4

-8

-12

Percent bias

DUDS Site

0 1 2 3 4 5

Number of intermediate exits

10

8

6

4

2

0

Coefficient of variation (percent)

DUDS Site

0 1 2 3 4 5

Number of intermediate exits

Figure 4—Evaluation of the bias and coefficient of variation of the SV 

estimator for a day-use developed site (DUDS) that is open from 6.00 

to 21.00 hours with 50 recreationists who will be last-exiting the site on 

that site day and arrived on the site during the site day (LERD) each with 

probability of capture of 0.9 for all exits. The pre-noon estimator (8.00 to 

14.00 hours) (solid line) and post-noon estimator (12.00 to 18.00 hours) 

(dashed line) are evaluated over a range of numbers of intermediate exits.
15

Conclusions

The ORUS model appears to be simulating the behavior 

incorporated into it by the various statistical distributions 

that describe the model components. Parameterization of 

the arriving and last-exiting beta distributions revealed the 

behavior patterns of the four different types of recreationists. 

A test simulation of behavior of recreationists at a DUDS

site correctly reflected the statistical distributions used for 

the model’s components. Further examination of several 

scenarios developed by altering the model’s parameters 

showed that a bias of considerable magnitude may be present

in many instances. Thus, use of the model to examine various

scenarios can help isolate problems and formulate refinements

in the survey methodology for future NVUM sampling.

These sample simulation results reveal some difficulties 

with the NVUM recreation use estimator. However, it should 

be kept in mind that ORUS is a very simple model at this 

point and does not yet make provisions for many problems 

that can occur in field sampling. For instance, the variation in the SV estimator does not provide for biases due to 

commuter traffic or to the “voluntary survey” sign effect that 

are believed to occur in the field. The effect of these biases 

on the estimate is unknown. Further refinements in the 

model are possible to help quantify these sources of bias and 

to make the recreationist behavior more realistic. 

Acknowledgments 

The authors acknowledge the help of the many Forest 

Service personnel who participated in the field sampling for 

the National Visitor Use Monitoring program.

References 

Cochran, W.G. 1977. Sampling techniques. 3d edition. New York: John 

Wiley. 428 p.

English, D.B.K., Kocis, S.M., Zarnoch, S.J., and Arnold, J.R. 2002. 

Forest Service national visitor use monitoring process: research method 

documentation. Res. Pap. SRS-57. Asheville, NC: U.S. Department of 

Agriculture, Forest Service, Southern Research Station. 14 p.

Zarnoch, S.J., Kocis, S.M., Cordell, H.K., and English, D.B.K. 2002. A 

pilot sampling design for estimating outdoor recreation site visits on the 

national forests. Res. Pap. SRS-29. Asheville, NC: U.S. Department of 

Agriculture, Forest Service, Southern Research Station. 20 p.

60

40

20

0

-20

Percent bias

GFA Site

0 1 2 3 4 5

Number of intermediate exits

20

18

16

14

12

10

8

6

4

2

0

Coefficient of variation (percent)

GFA Site

0 1 2 3 4 5

Number of intermediate exits

Figure 5—Evaluation of the bias and coefficient of variation of the SV 

estimator for a general forest area site (GFA) that is open from 6.00 to 

21.00 hours with 10 recreationists who will be last-exiting the site on that 

site day and were at the site before the official beginning of the site day at 

midnight (LERB), 10 recreationists who will be last-exiting the site on that 

site day and arrived on the site during the site day (LERD), 10 recreationists 

who will not be last-exiting the site on that site day and were on the site 

before the official beginning of the site day at midnight (NLERB), and 

10 recreationists who will not be last-exiting the site on that site day and 

arrived on the site during the site day (NLERD) each with probability of 

capture of 0.9 for all exits. The pre-noon estimator (8.00 to 14.00 hours) 

(solid line) and post-noon estimator (12.00 to 18.00 hours) (dashed line) are 

evaluated over a range of numbers of intermediate exits.
16
Zarnoch, Stanley J.; English, Donald B.K.; Kocis, Susan M. 2005. An outdoor 

recreation use model with applications to evaluating survey estimators. Res. Pap. 

SRS–37. Asheville, NC: U.S. Department of Agriculture, Forest Service, Southern 

Research Station. 15 p.

An outdoor recreation use simulator (ORUS) has been developed to simulate recreation 

survey data currently being obtained by the U.S. Department of Agriculture Forest 

Service, National Visitor Use Monitoring (NVUM) programʼs survey of the national 

forests of the United States. Statistical distributions represent the various behaviors of 

recreationists during their visit to a recreation site. The beta distribution is used to model 

arriving times and last-exiting times. The Poisson distribution is used to model the number 

of intermediate exits from the site, and the times of the exits are selected randomly 

according to the uniform distribution. Finally, three levels of trap shyness are assigned 

to the recreationists to quantify the probability that the recreationists will be captured by 

the interviewer. The beta distributions for arriving and last-exiting are parameterized to 

the NVUM survey data. The functioning of the simulator is demonstrated with a simple 

example. The utility of ORUS in evaluating the bias and coefficient of variation of various 

survey scenario estimators of recreation use is also presented.

Keywords: Last-exiting recreationist, National Visitor Use Monitoring, ORUS, 

simulation, trap shy.
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