bluuebunny/crossref_metadata_2025 huggingface dataset:
The Generalized Pair Chart for Right­Censored Observations
Authors: Agung Igusti Ngurah , Sen Pranab Kumar
Published: August 2016

The pair chart is known to be a convenient descriptive tool in comparing two samples and in calculating and interpreting various nonparametric procedures for the two­sample problem (see Quade (1973)). To incorporate rightcensored data in the two­sample problem, a generalized pair chart is considered and the same is utilized in the schematic computation of Gehan's W­statistic (Gehan (1965)) and a triplet statistic (see Crouse and Steffens (1969)) among others. An alternative pair chart based on partial observations is also considered. A maximal distance statistic, based on the generalized pair chart, has been considered for testing the hypothesis of equality of the two distributions.
Further Results on GGD Designs
Authors: Panandikar Sanjeev C.
Published: August 2016

In this paper we discuss some of the properties of the matrix ( NN') of the Generalised Group Divisible (GGD) design with λ ij ; i, j=l,2. The properties are the characteristic roots, the Hasse­Minkowski invariant and the nonexistence theorems. Some new methods for constructing GGD designs are also given.
Optimal Ordering Policies with Random Lead Time for a Perishable Item with Random Demand
Authors: Mukherjee S. P. , Chakraborty R.
Published: August 2016

A static inventory model with random demand for a product having two­period life in the face of random lead time has been developed. Optimal order quantities assuming uniform demand and lead time have been worked out.
D-Optimal Designs for Estimating the Optimum Point in a Multifactor Experiment
Authors: Mandal Nripes Kumar
Published: August 2016

The problem considered in this paper is that of estimating the maximal (minimal) point of a quadratic response surface. This problem was earlier considered by Chatterjee and Mandai (1981) where ‘deficiency of a design’ was used as a criterion for comparing different designs. Here we use the D-optimality crit rion in an extended sense and obtain designs under this criterion. Firstly, the design is obtained by an heuristic approach motivated by the symmetry of the problem. Finally, D-optimality is verified through a necessary and sufficient condition. The designs obtained are rotatable and are same as those for the deficiency criterion in a special case.
On Nested Row-Column Partially Balanced Incomplete Block Designs
Authors: Agrawal H. L. , Prasad Jagdish
Published: August 2016

A number of methods of construction of PBIB-RC designs, based upon the method of differences, are developed.
Admissibility of the Symmetrized Des Raj Estimator for Fixed Size Sampling Designs of Size Two
Authors: Sengupta S.
Published: August 2016

An estimator identical in form with the symmetrized Des Raj estimator based on a PPSWOR sampling design of size two is shown to be admissible within the class of all estimators of a finite population total for any fixed size sampling design of size two.
On the Limiting Behaviour of the Empirical Kernel Distribution Function
Authors: Sen Pranab Kumar
Published: August 2016

For an estimable parameter of degree m(⩾ 1), Glivenko-Cantelli lemma type result for the empirical kernel distribution and weak convergence of the related empirical process are studied. Some statistical applications of these results are also considered.
Estimation of Variance Component for one-way Classification with Heteroscedastic Error
Authors: Chatterjee Shoutir Kishore , Das Kalyan
Published: August 2016

For an unbalanced one-way classification under the random effect model where the error variance remains same within each class bttt varies over the classes, the problem of estimation of the variance component due to class effect is considered. A class of estimates including some estimates suggested from intuitive considerations is examined and it is shown that when the class size can assume only a finite number of distinct values, it is possible to set up an estimate which is asymptotically better than all the_ members of the class. Further, in the 1encral case it is shown that given any estimate belonging to a particular class, it is possible to find a corresponding estimate which is asymptotically bettor.
Admissibility of Unbiased Estimators in Finite Population Sampling for Samples of Size at Most two
Authors: Sengupta S.
Published: August 2016

A sufficient condition for admissibilitY is given for unbiased estimators of finite population parameters when sample size is at most two. The result is used to check admissibility of several unbiased estimators of population totals.
On the Application of Palm Probability for Obtatning Inter-Arrival Time Distribution in Weighted Poisson Process
Authors: Biswas Suddhendu , Pachal Tapan Kumar
Published: August 2016

The distribution of the time between the first and the n-th arrival given that the first arrival occurred at T-0 is derived for a compound Poisson process weighted by a Gamma distribution.
On new Classes of Rules for Selecting the Set Containing the Best Population
Authors: Naik Umesh D.
Published: August 2016

In this paper, new classes of rules are proposed for selecting from a given set of populations, a subset containing the best population. The rules have the following property: The probability that the selected set contains the best population is greater than or equal to P*, a preassigned number. The derivation of the rules is based on Schur concave functions. The rules apply to various types of distributions such as normal and gamma.
Fixed Length Interval Estimation of the Location Parameter of a Pareto Distribution
Authors: Ghosh Malay , Wackerly Dennis
Published: August 2016

A sequential fixed-width confidence interval for the location parameter of a Pareto distribution with unknown shape parameter is developed. The procedure Is shown to be asymptotically consistent and asymptotically efficient in the sense of Chow and Robbins (1965).
E-IG Model in Life Testing
Authors: Bhattacharya Samir K. , Kumar Santosh
Published: August 2016

A model for life time distribution, obtained by compounding the exponential distribution by the Inverse Gaussian distribution, has been studied.
A Note on a Parametric Relation of Variance Balanced Block Designs
Authors: Saha G.M. , Pal Samarandranath
Published: August 2016

The object of this communication is to prove the important parametric relation [Formula: see text] and hence [Formula: see text] for all connected Variance Balanced (VB) block designs, excepting the cquireplicatcd orthogonal designs which arc trivially VB.
Weak Convergence of Empirical Processes of Dependent Random Vectors Under Logarithmic Mixing Rates
Authors: Deo Chandrakant M.
Published: August 2016

It is proved that empirical processes of ø-mixing or Ψ-mlxing random vectors conv11rge to appropriate Gaussian processes under logarithmic mixing rates. A Kiefer-type bound on the tail-probabilities of empirical processes is also obtained under the same mixing rates.
s-Level Multiple-Response Main-Effects Factorial Plans
Authors: Batra U. , Aggarwal M.L.
Published: August 2016

This paper deals with construction of plans for s-level factorial experiments in which there are p response variables and each respose is affected by one or more factors. The plans are orthogonal for each response variable. Estimates of the parameters in the models for such plans are obtained when Σ, the dispersion matrix of an observation vector is known. The properties of these estimates can be of help in designing the experiment so that the variances of estimates of the parameters can be influenced by their relative importance.
Closure under Convolution of Dominance Relations
Authors: Mukherjee S. P. , Chatterjee A.
Published: August 2016

The closure of likelihood ratio (LR), failure rate (FR) and mean remaining life (MRL) orderings under convolution of distributions have been established in a restricted set up.
On the Limiting Behavior of a Random Walk
Authors: Rosalsky Andrew
Published: August 2016

[Formula: see text]

AMS (1980) Subject Classification: Primary 60F05, 60F15.
Simultaneous Estimation of Proportions in a Finite Population
Authors: Mukhopadhyay N. , Chattopadhyay S.
Published: August 2016

Sequential and multistage sampling strategies via simple random sampling without replacement, are proposed for simultaneously estimating several proportions in a finite population. Various asymptotic first-order properties are addressed, while some limited moderate sample performance have also been included.

AMS (1980) Subject Classification: Primary 62L99; Secondary 62L12
A Note on a Criterion for a Block Design to be X-1­Balanced
Authors: Mohan N. R. , Janhavi J. V.
Published: August 2016

An easy­to­verify criterion is proposed for a not necessarily connected block design to be X-1­balanced and its connection to the existing criteria is brought out. An example of a disconnected PBIBD is given which is X-1­balanced for a family of matrices X that includes a constant multiple' of identity matrix so that the PBIBD happens to be variance balanced.

AMS (1990) Subject Classification: 62 K 10
Optimal Repeated Measurements Designs Under Non-Additive Mixed Effects Models
Authors: Bose Mausumi
Published: August 2016

The robustness of some optimality results on repeated measurements designs is studied when tbe effect due to the units is random and an interaction due to the direct and residual effect of treatments is taken into account.
Computation of Statistical Distribution of Delay Time for G1/G/1 System
Authors: Ghosal A. , Barman Ashok Kumar
Published: August 2016

In queuing literature identification of delay time distribution is confined either to determination of its balance transformation or computation of its mean. This paper deals with the approximation of the distribution of its delay time under equilibrium conditions.
A Characterization of the Exponential Distribution
Authors: Jebvanand E. S. , Nair N. Unnikrishnan
Published: August 2016

In this note we prove that the exponential distribution is characterized by the property [Formula: see text] where Y is a future observation and x1, x2,…, x n are identical and independently distributed observations from a continuous population with density f( x; a), where a is assumed to have a non-informative prior distribution
A Cusum Test for Symmetry Against Positive Biasedness
Authors: Aly Emad-Eldin A. A. , Kochar Subhash C.
Published: August 2016

Let X be a random variable with an absolutely continuous distribution function F(.) and density function f(.). We propose and study a cusum test for testing the symmetry of X around zero against the one-side alternative H1 : f( x ) ⩾ f(- x ) for all x ⩾ 0 with strict inequality for some x. The proposed test is distribution-free under the null hypothesis. The null distribution of the proposed test is given. A Monte Carlo simulation study to compare the power of the proposed test with other one-sided tests for symmetry is reported.
Simultaneous Estimation of Poisson Means under Weighted Entropy Loss
Authors: Chung Younshik , Kim Chansoo , Dey Dipak K.
Published: August 2016

Let X1, ... , X p be p independent Poisson random variables. The problem is to 5imultaneously estimate the unknown parameters under the weighted entropy loss. Two different classes of dominating estimators are obtained by solving certain difference inequality. Using Monte Carlo method, we compute the risk improvement for the simultaneous estimation of the Poisson means.
Classification of Grab Samples Using Composite Sampling: An Improved Strategy
Authors: Sengupta Soma , Neerchal Nagaraj K.
Published: August 2016

Samples are drawn from the entire bulk and are to be classified into those exceeding a given level of toxic and those under compliance. Measuring the composites (a mixture of original samples) instead of the original grabs leads to cost reduction. Using an idea often used in group testing, we demonstrate that the classification can be carried out based on the composite measurements. We also investigate misclassification probabilities of these strategies.
Estimation of the Smaller and Larger of Two Exponential Location Parameters with a Common Unknown Scale Parameter
Authors: Carpenter Mark , Pal Nabendu
Published: August 2016

Assume independent random samples are drawn from two populations which are exponentially distributed with unknown location parameters and a common unknown scale parameter. The interest in this paper is to estimate the minimum and maximum of the unknown location parameters. Several estimators are proposed and their properties in terms of MSB and absolute bias are studied and compared.
Some Nonparametric Group Sequential-Type Tests for Two Population Problems
Authors: Bandyopadhyay Uttam , Biswas Atanu
Published: August 2016

In the present paper we propose some group sequential-typo nonparametric tests for clinical trials with two treatments by taking observations in pairs and by adopting an inverse binomial scheme of sampling. Competitors of the proposed tests are aiso obtained. Exact and asymptotic results on some performance characteristics of the tests are studied and examined. Unbiasedness and consistency of the proposed tests are also studied.
Estimation of the Common Mean of Two Normal Populations Using Two Stage Sampling
Authors: De Moloy , Sarkar Jyotirmoy
Published: August 2016

We exhibit the superiority of the Graybill- Deal estimator for estimating the common mean of two univariate normal populations with unequal variances, under a two stage sampling scheme. Some properties of the two-stage Graybill-Deal estimator are discussed.
The Geometry of Estimating Functions in the Presence of Nuisance Parameters 1
Authors: Chan Schultz , Ghosh Malay
Published: August 2016

The paper studies the geometry of estimating functions in the presence of nuisance parameters. The basic technique involves an idea of orthogonal projection first introduced by Small and McLeish (1989, 1991, 1992, 1994) in this context. The three main topics are : (A) globally optimal estimating functons; (B) locally optimal estimating functions; (C) conditionally optimal estimating functions. A general result is derived in each case. As special cases, we extend and unify some of the results already available in the literature. In particular, as special cases of our result on globally optimal estimating functions, we find the results of Godambe and Thompson (1974) and Godambe (1976) with nuisance parameters. We provide also a geometric interpretation of conditional and marginal inference of Bhapkar (1989, 1991) and Lloyd (1987) . As application of our result on locally optimal estimating functions, Godambe's (1985) result on optimal estimating functions for stochastic processes is extended to nuisance parameters. Finally, our general result on conditionally optimal estimating function helps to generalize the findings of Godambe and Thompson (1989) to situations which admit the presence of nuisance parameters.
Some E-Optimal Partially Balanced Nested Row-Column Designs with Unequal Block Sizes
Authors: Uddin Nizam
Published: August 2016

For ten and fewer number of treatments, a total of 298 equireplicate E-optimal Dellted row-column designs with at most two unequal blocbizes are given.
Analysis of a Bulk Demand Two Commodity Inventory Problem
Authors: Krishnamookthy A. , Joseph Merlymol , Ravindranathan
Published: August 2016

A continuous review, bulk demand, two commodity inventory problem is investigated. It is assumed that the probability for a demand of both the commodities together is zero. Replenishment is instantaneous and no shortage ia permitted. The time dependent ByBtem Bize probabilities and their limiting behaviour are investigated. An optimisation problem aaociated with the model is studied. An example is provided. Some numerical illustrations are given.
LBI Tests for the Detection of General Compound Distributions
Authors: Durairajan T.M. , Raman K.J.
Published: August 2016

The locally best invariant (LBI) test for the detection of “Compound Departures” from the general compound distributions is constructed. This LBI test is an optimally robust test for the models in Durairajan and Raman (1996 a,b) . Further, the present model generalizes the particular cases considered by Sen Gupta and Pal (1991, 1993) and Durairajan and Raman (1996 a,b) among others.
Estimation of Finite Population Transition Probability Matrix Based on Two Stage Sampling Design
Authors: Chakrabarty Tapan Kr. , Singh B.M. , Tripathi T.P.
Published: August 2016

We consider the problem of estimation of the transition probabilities of a Markov chain from survey data based on a complex sampling design. A finite population estimation procedure for estimating the transition probabilities of a finite state time-homogeneous bivariate Markov chain, that may be used to model an intergenerational social mobility problem, is presented. The estimators based on two stage sampling design when both the first stage and second stage samples are selected according to simple random sampling without replacement are proposed. We provide the bias and mean square error of the proposed estimators. Further, based on empirical data we also calculate the estimated biases and estimated mean square errors.
Some Results on the Curse of Dimensionality and Sample Size Recommendations
Authors: Dasgupta Anirban
Published: August 2016

Multivariate density estimation is well known to be a tremendously difficult problem due to the occurrence of phenomena commonly known as the corner effect and the curse of dimensionality. Specifically, histogram density estimation in high dimensions is plagued by the consequence that sampled observations tend to reside with high probability in low density regions of the sample space. In this article we attempt to quantify two central things: in how many dimensions, one starts to really feel the curse of dimensionality, and what sort of sample sizes are needed to do any kind of a reasonable inference in various dimensions. These questions cannot be formulated in a unique way. So the attempt is to derive a broad spectrum of results, which are then illustrated by extensive computation. A number of results may be of independent interest in combinatorics and applied probability. Our subjective conclusion after these extensive computations is that in 3 dimensions one often sees the most drastic effect relative to just one less dimension; in 5 dimensions one feels the curse of high dimensions rather strongly; in 10 dimensions, the feasibility of inference with realistic sample sizes basically vanishes. We also give a subjective minimum sample size recommendation based on the number of dimensions. These calculations are different in character from Epanechnikov(1969).

AMS (2000} Subject Classification: Primary 62H05; Secondary 62G07.
Estimation for some Stochastic Partial Differential Equations Based on Discrete Observations
Authors: Rao B.L.S. Prakasa
Published: August 2016

Stochastic partial differential equations (SPDE) are used for stochastic modelling, for instance, in the study of neuronal behaviour in neurophysiology and in building stochastic models for turbulence. Huebner, Khasminskii and Rozovskii (1993) started the investigation of the maximum likelihood estimation of the parameters involved in two types of SPDE's and extended their results for a class of parabolic SPDE's in Huebner and Rozovskii (1995). Prakasa Rao (1998,2000) obtained Bernstein - von Mises type theorems for a class of parabolic SPDE's and investigated the properties of Bayes estimators of parameters involved in such SPDE's. In all the papers cited earlier, it was assumed that a continuous observation of a random field uε( x, t) satisfying the SPDE over the region [0, 1] × [0, T] is available. It is obvious that this assumption is not tenable in practice and the problem of interest is to develop methods of estimation of parameters from the random field uε( x, t) observed at discrete times t and at discrete positions x or from the Fourier coefficients uiε( t) observed at discrete time instants. We construct consistent and asymptotically normal estimators of the parameter based on the Fourier coefficients uiε( t) observed at discrete times [Formula: see text] tends to infinity.

AMS (2000) Subject classification: Primary 62 M 40; Secondary 60 H 15.
An Optimum Ordering Policy and its Estimation in a Two-Supplier Inventory Model with Uncertainties in Supply
Authors: Mitra Murari , Basu Sujit K.
Published: August 2016

We consider a single-item one-period inventory model where the market demand is assumed to be random and the item under consideration is obtained from two suppliers who also supply random amounts with means equal to the order placed to the supplier concerned. Under new better than used in expectation (NBUE) assumption on the supply distributions, possibly different, a strategy which maximizes a minimum profit has been proposed. An estimate for this maximin order quantity whenever the (customer) demand distribution is unknown has been obtained and strong consistency of the suggested estimator established.

AMS (2000) Subject Classification: Primary 90B05; Secondary 62G99, 60F15.
On Single Server Vacation Queues with Deterministic Service or Deterministic Vacations
Authors: Madan Kailash C. , Saleh Mohammad F.
Published: August 2016

We study two models of a single server queue with vacations. In model A, we study an M ⁄ M ⁄1 queue with deterministic vacations and designate it as M⁄ M⁄ D⁄l queue and in model B we study an M⁄ D⁄1 queue with exponential vacations and designate it as M⁄ D⁄ M⁄1 queue. We obtain time dependent as well as steady state probability generating functions for both the models. For the steady state, we obtain explicit results for the mean number in the system and the mean waiting times for both models. All known results of the M ⁄ M ⁄1 and the M⁄ D⁄1 queues are derived as special cases.
Successive Sampling Using Auxiliary Information on Both the Occasions
Authors: Biradar R.S. , Singh H.P.
Published: August 2016

In successive sampling with partial replacement, an estimator is proposed for the population mean on the second of two successive occasions utilising information available on both the occasions on an auxiliary variate with an unknown population mean. It is shown that the proposed estimator is more efficient than the sample mean and the estimators considered by Sen (1971). An empirical study is also included.
A Subordinated Process with Geometric Exponential Operational Time
Authors: Lekshmi V. Seetha , Jose K.K.
Published: August 2016

In this note a subordinated process with Geometric Exponential operational time is introduced and studied.
Construction of E (fNOD)-Optimal Supersaturated Designs VIA Room Squares
Authors: Fang Kai-Tai , Ge Gen-Nian , Liu Min-Qian
Published: August 2016

Supersaturated design is essentially a fractional factorial in which the number of potential effects is greater than the number of runs. And Room square is an important object in combinatorial design theory. We show a link between these two apparently unrelated kinds of designs. E ( fNOD) criterion for comparing supersaturated designs is proposed and a lower bound of E ( fNOD) is obtained as a benchmark of design optimality. It is shown that the E ( fNOD) criterion is an extension of the popular E( s2) and ave x2 criterion (for two- and three-level supersaturated designs respectively). A new construction method for multi-level supersaturated designs via Room squares is also proposed and some properties of the resulting designs are investigated.
Lan Based Asymptotic Theory for Time Series
Authors: Taniguchi Masanobu , Puri Madan L.
Published: August 2016

The local asymptotic normality (LAN) , introduced by LeCam, is the most fundamental concept in the statistical asymptotic theory. If LAN property for a class of statistical models is established, then the asymptotic optimality of estimator and test can be described in terms of the central sequence. This concept gives a unified view for the statistical estimation and testing theory. Recently the LAN concept has been introduced to the asymptotic theory for time series. This paper provides a personal overview of the LAN results for linear processes, nonlinear processes, diffusion processes, long-memory processes, and locally stationary processes, etc.. The results are applied to the asymptotic estimation, testing theory, and discriminant analysis in time series. Then, construction of asymptotically optimal estimator, test and discriminator is discussed.
Optimal Choice of Design Parameter in an Adaptive Design
Authors: Bandyopadhyay Uttam , Biswas Atanu
Published: August 2016

Adaptive designs are occasionally used in clinical trials for allocating entering patients between two treatments. The randomized playthe- winner rule is such an adaptive design originally introduced by Wei and Durham (1978) and Wei (1979) . The present paper provides an optimal choice of design parameter for such a rule with reference to the Michigan ECMO trial, a real life application of the rule. Finally, choice of design parameter in a more general situation is also discussed.
On Reflected Backward Stochastic Differential Equations
Authors: Ramasubramanian S.
Published: August 2016

Some aspects of reflected backward stochastic differential equations in a half-line or in an orthant are surveyed. The roleof an optimal stopping problem in solving RBSDE in a half-line is highlighted. RBSDE in an orthant with time-space dependent oblique reflection is formulated and an outline of the ideas involved in proving the existence of a unique solution is given.
Discretization of Continuous Distributions with an Application to Stress-Strength Reliability
Authors: Roy Dilip
Published: August 2016

A generic approach has been studied for discretization of continuous distributions in the univariate and bivariate situations. In particular, discretization of uniform distribution has been used to develop a bivariate binary model. Characterization results have also been studied to establish a direct link between the discrete Weibull distribution and its continuous counterpart. Attempts have also been made for approximating reliability of complex systems using suitably adjusted discrete concentrations of continuous design variables.
Complex am Model for Non Stationary Speech Signals
Authors: Nandi Swagata , Kundu Debasis
Published: August 2016

Recently complex Amplitude Modulated model in presence of additive white noise was used to analyze certain non-stationary speech data. It is observed that the assumption of white noise may not be proper in many cases. In this paper we consider the complex Amplitude Modulated signal model in presence of stationary noise. We consider the least squares estimators and the estimators obtained by maximizing the Periodogram function. The two estimators are asymptotically equivalent. We study theoretical properties of both these estimators and observe their performances through numerical simulations. One speech data is analyzed and it is observed that the performance of the proposed estimators are quite satisfactory.
A Test of Exponentiality in Life-Testing Against Weibull Alternatives Under Hybrid Censoring
Authors: Das Biswanath , Nag Asim Sankar
Published: August 2016

In this study, a test for exponentiality in life-testing against Weibull IFR⁄DFR alternatives based on observed number offailures has been suggested using a hybrid censoring scheme under which for a given size α, the test is terminated as soon as a pre-assigned number r of failures occur, or a pre-assigned time tr, α elapses, whichever is earlier. The optimal censoring parameters ( r, tr, α) have been numerically obtained for selected choices of the sample size n and the test-size α as minimax solutions under a squared error loss function. The performance of the suggested test has been compared with that of the test based on the maximum likelihood estimator suggested by Thoman, Bain and Antle (1969) in terms of power and average testing time for selected situations.
Slope Rotatability with Correlated Errors
Authors: Das Rabindra Nath
Published: August 2016

In Das (Cal. Statist. Assoc. Bull. 47, 1997. 199 -214) a study of second order rotatable designs with correlated errors was initiated. Robust second order rotatable designs under autocorrelated structures was developed. In this paper, general conditions for second order slope rotatability have been derived assuming errors have a general correlated error structure. Further, these conditions have been simplified under the intra-class structure of errors and verified with uncorrelated case.
A Stocking CUM Pricing Model under the Effect of Consumer Behaviour
Authors: Dutta Suddha Sankar , Pal Manisha
Published: August 2016

The paper considers a dynamic risk model with periods of equal length for stocking and selling products where the selling price of the stocked item is under control of the management. A preset price ( y) may appear unsatisfactory to a fraction (1- ψ( y)) of the arrived demand and this fraction of demand is lost irrespective of the stock on hand. The other fraction ( ψ( y)) of the demand is retained if there is stock on hand and in case of stockout a fixed fraction ( π) of the demand, is backlogged whereas (1 - π) of the unmet demand is lost. ψ( y) is decreasing in y. where y is at least as high as the procurement cost, and both ψ( y) and π are either known or can be estimated from past experience. Arrival of demand over a reorder interval is continuous, following some known probabilistic Jaw and is independent of price. Optimal values of stock height and selling price have been obtained through maximization of profit, given that both of them are to be set at the beginning of a reorder interval.
A Simple Statistical Method for Recognition of Hand-Written Numerals
Authors: Ghosh Arka P.
Published: August 2016

We explore a simple statistical method for classifying handwritten numerals. We work with numerals only in segmented form. We defined a pseudodistance function between handwritten numerals and classify each numeral based on its distance from the those in the reference set. This method, and its obvious variants, are studied on the basis of their performance on a data-set of moderate size (95 observations). The results suggest that this method may be considered in recognition of handwritten numeric characters.
On Two Novel Applications of Ranked Set Sampling
Authors: Sarikavanij Sukuman , Tiensuw Montip
Published: August 2016

In this paper we discuss two case studies which clearly indicate the advantages of using a ranked set sample (RSS) over those of a simple random sample (SRS). The applications of RSS considered here cover single family homes sales data, and tree data. It is demonstrated that in each case RSS is much more efficient than SRS for estimation of population mean.
Estimation from an Under-Covered Sample in a Complex Survey for Auditing
Authors: Chaudhuri Arijit
Published: August 2016

We encounter a practical problem when from a finite population a complex survey design justifies selection of a sample in five stages. The design stipulates selecting a specified number of n(> 2) first stage units by Rao, Hartley and Cochran's (RHC, 1962) scheme followed by simple random sampling (SRS) without replacement (WOR) in each of the four subsequent stages. At the implementation stage a resource crunch calls for reducing the first stage sample size from n to m ( m < n). The consequential modifications in the methods of estimation of population total, mean and ratio of two totals and those of the variance of the first and the mean square errors of the latter two estimators are spelt out. The problem arises in the context of designing audits of Government documents by appropriate sampling.
Non-Linear Time Series Modeling of Volatile Onion Price Data Using AR(p )-ARCH( q)-In-Mean
Authors: Ghosh Himadri , Prajneshu
Published: August 2016

Onion prices have been in the headline since 1998 for its tear jerking effect on consumers, farmers and Government alike. Present paper attempts to develop a realistic time-series model to explain the behaviour of monthly onion price data during April, 1996 to October, 2001 collected from National Agricultmal Cooperative Marketing Federation (NAFED), New Delhi. In the first step, attempts are made to apply Seasonal Autoregressive (SAR) model to the detrended data. However, residual analysis reveals that assumption of constant one-period ahead forecast variance does not hold true. Accordingly, a new class of stochastic processes, called Autoregressive Conditional Heterosqedastic (ARCH) process, is studied to model the residual series. To this end, computer programs are written in EViews and package, Version 4.0 and IML in SAS, Version 8e to perform Lagrange-Multiplier test for possible presence of ARCH, to fit the AR(p )- ARCH( q) model, and to carry out residual analysis after fitting ARCH model. It is shown that ARCH model provides a good description of the data under consideration. Finally, the identified model is employed for forecasting purposes.
Analysis of Scoring Rate in a Limited Over Cricket Match
Authors: Guha Apratim
Published: August 2016

In their work for resetting targets for rain-truncated limited over cricket matches, Duckworth and Lewis (1998} use a probabilistic model with remaining wickets per ball as the explanatory variable. Here we present a preliminary study of a reasonahly simple model for scoring rate in a limited over cricket match with the above and some added explanatories. The model is fit for only the first innings of the game and some minor modifications are suggested for the second innings.
Optimal Assembly Problem of Rotor Blades : A Heuristic Approach
Authors: Dasgupta R. , Ghosh J. K.
Published: August 2016

Consider the optimal assembly problem of assigning blades of different but known momenta to fixed positions of a rotor of circular cross section used in hydroturbine. The assembly has to be such that the resultant imbalance of the rotor after assembly is a minimum and the momenta are more or less uniformly spread over the circular section. When the number of blades and consequently the number of possible permutations is also large , the optimal assembly is difficult to obtain. A few heuristic approaches for the assembly are suggested and the statistical properties for the assembly arc studied under an appropriate data based model (for the distribution of momenta). We compare the performance of the proposed techniques with the optimal arrangement when the number of blades is small. It is also found that the imbalance arising out of the proposed assembly can be predicted with a high degree of accuracy. based only on first a few large momenta spacings when the blade momenta follow sowe standard distributions.
On the Beta Record Values
Authors: Nadarajah Saralees , Ahsanullah Mohammad
Published: August 2016

Explicit algebraic expressions are derived for computing the means, variances and the covariances of the record values from a beta distribution. The derivation uses a representation theorem due to Bairamov and Ahsanullah (2000) and a series expansion for the inverse function of the standard beta cdf. The results generalize those presented in Nadarajah and Ahsanullah (2004) for the arc-sine distribution.
Geometric Infinite Divisibility and the Waiting Time Paradox
Authors: Pillai R.N. , V. R. Saji Kumar
Published: August 2016

It is shown that the waiting time W in a stationary renewal process generated by X has the form W = X+ Y, with Y non­negative independent of X if and only if X is a geometrically infinitely divisible random variable. This is an improvement over Van Harn and Steutel (1995) where the converse is left unproved .
Prediction in Two­Equation Linear Regression Models
Authors: Dey Amitava , Sharma V. K. , Ghosh Himadri
Published: August 2016

In regression models using time series data, the errors are generally correlated. The sample residuals contain useful information for predicting post­sample observations. This information, which is generally ignored, has been exploited here in deriving the best linear unbiased predictors in a 2­equation linear regression model. The gain in efficiency of the proposed predictors over the usual generalized least ­ squares predictors has been obtained and the particular case when error terms in the two equations follow AR(l) process has also been disscussed.
On the Characteristic Function of the Product of Gamma and Rayleigh Random Variables
Authors: Nadarajah Saralees , Ali M. Masoom
Published: August 2016

The distribution of products of random variables arises explicitly in many areas of the sciences, engineering and medicine. This has increased the need to have available the widest possible range of statistical results on products of random variables. In this note, we study the distribution of XY when X and Y are gamma and Rayleigh random variables by deriving various explicit expressions for its characteristic function. An application of the results is provided to drought data from Nebraska.
Weak Laws for Weighted Sums of Row Pairwise NQD Sequences of Random Variables
Authors: Cai Guang­Hui
Published: August 2016

In this paper , we study the weak laws for weighted sums of row pairwise NQD sequences of random variables. The results obtained not only generalize the results of Beak (2003) to row pairwise NQD Sequences, but also improve them.
Convergence of a Robbins-Monro Algorithm for Recursive Estimation with Non-Monotone Weights for a Function with a Restricted Domain and Multiple Zeros
Authors: Findley David F.
Published: August 2016

Summary

Convergence properties are established for the output of a deterministic Robbins- Monro recursion whose function can have singularities and multiple zeros. Our analysis is built largely on slight adaptations of some lemmas and proofs of Fradkov published only in an untranslated Russian monograph (Derevitzkii and Fradkov , 1981). A gap in Fradkov's proof of the final lemma is fixed but only for the scalar case. Our results can be applied to results of Cantor (2001) to establish the convergence of two well-known time series model recursive estimation schemes in the case of an incorrect moving average model. For such models, it is known that maximum likelihood estimates can converge w .p.1 to a set of values rather than to a single value. When the limit set is finite, our results show that , on a given realization of the time series, the (recursive) estimates will converge to single value. This is the first result establishing that estimates of a moving average coefficient do not oscillate forever among different limit set values when there are more than one.
Mixed Level Dispersion Experiments
Authors: Chatterjee Kashinath , Fang Kai-Tai
Published: August 2016

Summary

Rosenbaum (1996) and Hedayat and Stufken (1999) considered the construction of compound orthogonal arrays for the two-level factors which are useful in the study of dispersion experiments, pioneered by Taguchi (1986). This paper provides a general method of constructing such arrays and their applications to obtain several asymmetric compound orthogonal arrays for mixed level dispersion experiments. Such arrays are also found to be universally optimal even if the model includes some more parameters.
Weak Records of Geometric Distribution
Authors: Ahsanullah M.
Published: August 2016

Summary

Upper weak record values from a sequence of independent identically distributed random variables are considered. Several distributional properties of the upper weak records from geometric distribution are presented. Based on these distributional properties some characterizations of the geometric distribution are given.
Modeling of Material Wastage by Ornstein-Uhlenbeck Process
Authors: Dasgupta Ratan
Published: August 2016

Consider the problem of modeling the proportion wastage arising out of trimming the edges of paper and metal sheets to give these a regular shape. It is observed that curved edges in such cases may follow the sample path of a Ornstein- Uhlenbeck process. The production characteristic can then be expressed in terms of the parameters of the process which are estimable from the observed shape of the edge. Sample edge trajectories of two production processes are analysed and the production efficiency is interpreted in terms of proportion wastage.
Single Server Queue with Batch Arrivals and α - Poisson Distribution
Authors: R. Saji Kumar V. , Pillai R.N.
Published: August 2016

We consider a single server non-Markovian queueing system with α - Poisson arrivals and server vacations. When α = 1, it reduces to the usual Mx | G | 1 model with batch arrivals.
Precision Diagnostics in Regression Modelling
Authors: Shobha B.
Published: August 2016

In this paper, we consider a linear regression model with intraclass correlation structure and study the behaviour of the precision diagnostic statistic COVRATIO as a function of the intraclass correlation coefficient ρ. Interestingly, it turns out that for the model with intercept, COVRATIO is a monotonically decreasing function of ρ. Thus if the model errors have larger correlation, then it is more stable with regard to deletion of observations. We have also considered the ratio of traces TRATIO of the least squares estimator of the parameter vector under data reduction and without da.ta reduction. This ratio is also decreasing in ρ implying that loss of precision when model errors have the same high correlation is smaller when an observation is deleted. Lastly, we have determined the linear parametric function (LPF) whose BLUE is affected the most by data reduction.
Self Exciting Threshold Autoregressive Models for Describing Cyclical Data
Authors: Ghosh Himadri , Sunilkumar G. , Prajneshu
Published: August 2016

We thoroughly study a very important family of nonlinear timeseries models, viz. Self exciting threshold autoregressive (SETAR) types of models. A heartening feature of this family is that it is capable of describing cyclical data. As an illustration, SETAR models are then applied to country's lac export data during the period 1900-2000, obtained from Annual reports of Shellac Export Promotion Council, Kolkata. It is shown that fitted model, based on minimum Akaike information criterion (AIC), exhibits a threshold behaviour. Finally, attempts are made to obtain optimal predictor for out-of-sample data based on fitted SETAR model, which is found to be quite satisfactory.
Test for P(X < Y) in Two Stage Data Dependent Allocation Design
Authors: Bandyopadhyay Uttam , Das Radhakanta
Published: August 2016

The present article is related to test for P( X < Y) , where X and Y are two independent random variables having some continuous distribution functions (d.f.s). We consider a data dependent ethical allocation design where the observations on X and Y are drawn sequentially in two stages. For such design, we provide an asymptotically distribution free test procedure along with various asymptotic results. This design is compared with the usual single stage equal allocation design through the performances of the respective test procedures. The proposed design is also illustrated by using a real life data set.
Weighting and Prediction in Sample Surveys
Authors: Little Roderick J.
Published: August 2016

A fundamental technique in survey sampling is to weight included units by the inverse of their probability of inclusion, which may be known (as in the case sampling weights) or estimated (as in the case of nonresponse weights or post-stratification) . The technique is closely associated with the design-based approach to survey inference, with the idea that units in the sample are representing a certain number of units in the population. I discuss weighting from a modelling perspective. Some common misconceptions of weighting will be addressed, including the idea that modelers can ignore the sampling weights, or that weighting necessarily reduces bias at the expense of increased variance, or that units entering the calculation of nonresponse weights should be weighted by their sampling weights. A robust model-based perspective suggests that selection weights cannot be ignored , but there may be better ways of incorporating them in the inference than via the standard Horvitz-Thompson estimator and its variants.
On the Predictive Nature of Absolute Changes
Authors: Basak Gopal K. , Chung Leung-Chi , Lau Kai-Hon
Published: August 2016

Practitioners have often observed that it is easier to predict the absolute value of the change more accurately than predicting. the actual value. Here we give theoretical justification of the above observation using a couple of simple Autoregressive models. \Ve also show this by simulation and using our theory on real data.
Some Properties of Income Gap Ratio and Truncated GINI Coefficient
Authors: Nair N. Unnikrishnan , Nair K. R. Muraleedharan , Haridas Haritha N.
Published: August 2016

The income gap ratio and truncated Gini coefficients play an important role in the construction of poverty and affluence indices. In this paper we examine the question of determining the form of the income distributions based on the income gap ratio or truncated Gini coefficient for a given population and answer them in affirmative. We also discuss the behaviour of the Sen poverty index with respect to the head count ratio and the parameters of some selected income distribution models.
On Some Determinants for Distributive Justice in Children : A Study Based on Three States of India
Authors: Karmakar Rita , Ghosh Anjali , Dewanji Anup
Published: August 2016

Distributive justice is concerned with the way resources are allocated in an identified group (Tyler and Smith, 1998) . It is assumed that justice concepts would be related to cognitive-moral development. At the same time, justice rule preferences seem to be the results of parental practices. The present study aims to find out the effect of demographic determinants such as maturity (measured in terms of age), gender, regional variation and socio-cultural determinant (i.e., parenting style} on distributive justice of school students. Three groups of school students (boys and girls) are selected from West Bengal and two different states of North-Eastern India, namely, Meghalaya and Tripura. Distributive Justice Scale of Enright, Franklin and Manheim (1980) and Parental Authority Questionnaire of Leman (2005) are used in this study. Ordinal regression results indicate that the probability of choosing higher categories of distributive justice is significantly greater in case of older students than younger students. Regional variation also plays an important role in the development of distributive justice of students. Probability of choosing higher categories of distributive justice is higher in case of West Bengal students than the students of Meghalaya and Tripura. Among three different parenting styles, only permissive parenting style is significantly negatively correlated with distributive justice. High scores on permissive parenting style decrease the probability of choosing the higher categories of distributive justice. Thus the study indicates that not only demographic variables, such as maturity and regional variation, but also socio-cultural variable such as parenting style play important role in the development of children's idea of fairness concept. It also implies that permissive parenting style inhibits the development of fairness concept in children.
Some Aspects of Multivariate Behrens-Fisher Problem
Authors: Park Junyong , Sinha Bimal
Published: August 2016

In this paper we discuss the well known multivariate Behrens-Fisher problem which deals with testing the equality of two normal mean vectors under heteroscedasticity of dispersion matrices. Some existing tests are reviewed and a new test based on Roy's union-intersection principle coupled with the generalized P-value is proposed. The tests are compared with respect to size and power based on simulation, and applied to a few useful data sets.

AMS (2000) Subject Classification : 62H10, 62H15.