bluuebunny/crossref_metadata_2025 huggingface dataset:
Variations on a Bhattacharyya Theme
Authors: Arnold Barry C.
Published: August 2016

Bhattacharyya introduced a family of bivariate distributions with normal conditions in 1943. He discussed what additional conditions are required to guarantee that the joint distribution is a classical bivariate normal distribution. The family of distributions with normal conditionals is , in itself, an interesting exponential family. Its structure is discussed in the present paper. Extensions to higher dimensions and to cases in which the conditional distributions are prescribed to belong to non normal families are discussed. These conditionally specified families of distributions are shown to be particularly suitable for use as prior distributions in multiparameter Bayesian Inference settings.
Construction of Non-Proper Balanced Bipartite Block Designs
Authors: Jaggi Seema , Parsad Rajender , Gupta V.K.
Published: August 2016

The purpose of this paper is to give some methods of construction of balanced bipartite block designs. These designs are useful for comparing a set of test treatments to a set of control treatments. The methods of construction of non-proper balanced bipartite block designs are based on the UBe of incidence matrices of block designs with known patterns, such as balanced incomplete block (BiB) designs, group divisible (GD) designs and variance balanced (VB) designs. Using resolvable BIB designs and certain GD designs, two methods of construction of proper balanced bipartite block designs have also been given.
Robust Second Order Rotatable Designs Part II (RSORD)
Authors: Das Rabindra Nath
Published: August 2016

This paper is a sequel to Daa (1997} wherein a study of robust second order rotatable designs with correlated errors was initiated. Second order rotatability conditions were derived for general correlated error structure and special cases were examined under autocorrelated structure of errors.

Here we examine robustness of usual second order rotatable designs i.e., those with uncorrelated errors ( SORD's) with emphasis on properties such as weak rotatability (arising in the context of correlated error structure}, with due consideration of the cost involved.
An Alternative Class of Estimators in Double Sampling Procedures
Authors: Sahoo J. , Sahoo L.N.
Published: August 2016

Given that we know the population mean of an additional auxiliary variable z, we formulate a class of estimators for the finite population mean when the population mean of the main auxiliary variable x is unknown using a double sampling procedure. The class covers a wide range of estimators and acts as a complementary in a certain sense to the class suggested by Sahoo and Sahoo (1993).
On Computation of Probable Maximum Precipitation
Authors: Deshpande N.R. , Gore A.P.
Published: August 2016

Probable Maximum Precipitation (PMP) is a characterilltic of rainfall at a station that ia crucial in designing water impounding structures. Two alternative methode of its computation are described and compared with the statilltical-empirical technique due to Hershfield, generally used in India. One method is baaed on the Gumbel distribution, whilst the other is a modified version of the Hershfield technique. Both alternative methods are more objective and the atatiatical method admits direct interpretation. The currently used method appears to give an overestimate of PMP in all regions of India except the eouthern part.
On Partial Balance with Orthogonal Sub-Factorial Structure
Authors: Das Premadhis , Chatterjee Banibarna
Published: August 2016

The factorial effects have been partitioned into sub-factorial effects introducing groups among the levels of the factors and the C matrix of a design has been characterised so that these sub-effects are orthogonally estimable with partial balance. The particular case when the number of levels can be factorised has been seen to be of special interest.
A Multiserver Poisson Queue with a General Startup Time Under N-Policy
Authors: Borthakur Arun , Choudhury Gautam
Published: August 2016

This paper deals with the steady state behaviour of an M⁄M⁄c queueing system with a general startup time under N-policy, where the system is turned off as soon as the system becomes empty and turned on again when the queue size becomes ‘ N’. The service of the first customer in each busy period is always preceded by a random startup time (during which no proper work is done) to gearup the system. We place our emphasis on understanding the operational characteristic of the queueing system and derive the probability generating functions of the queue size distribution and joint distribution of the number of arrivals and startup time. Also, we provide appropriate interpretation of the queue size distribution and other performance measures. Finally, we verify some results of M⁄M⁄1 queueing system with general startup time under N-policy.
Generalised Balanced Matrices and Their Applications
Authors: Sastry D.V.S.
Published: August 2016

A method for constructing Generalised Balanced Matrices (GBM) is given and with the help of these GBMs, some families of PBIB designs are constructed.
Ciphertext Only Attack on LFSR Based Encryption Scheme
Authors: Maitra S. , Roy B. K. , Sarkar P.
Published: August 2016

Here a security attack on LFSR based stream cipher systems is described. The attack depends on some weakness of the memory less Boolean combining function used in the system and breaks the key using only the ciphertext. Siegenthaler used a correlation measure to define certain statistical test for finding out feasible keys. This can also be interpreted as testing the independence of two binary bit sequences. Here we extend the statistical test eonsidering the joint conditional probability of more than one binary random variables. We diacuaa algorithms with an example of non correlation immune function in the esse of three LFSRs and a multiplexer as a nonlinear combining function. Next we extend the method for correlation immune functions and illustrate that with suitable example. The motivation here is to present an applicetion of statisticsl method in cryptanalysis. Theoreticsl questions have been posed to motivate future research in this direction.
Some Properties of the Hellinger Distance Between Two Finite Sets of Distributions
Authors: Ahmad Ibrahim A.
Published: August 2016

[Formula: see text]
Smooth Isotonic Estimation of Density, Hazard and MRL Functions
Authors: Chaubey Yogendra P. , Sen Pranab K.
Published: August 2016

Incorporating the classical smoothing lemma of Hille (1948) , as adapted in Chaubey and Sen (1996), smooth isotonic estimators of density, hazard, mean residual life, and other functionals of (survival) distribution functions are proposed here. Along with the computational aspects, their (asymptotic) properties are discussed. Some extensions to the case of random censoring are also considered.
Large Second-Order Properties of a Two-Stage Point Estimation Procedure for the Range in a Power Family Distribution
Authors: Mukhopadhyay Nitish , Cicconetti Greg
Published: August 2016

In this article, a new two-stage sampling methodology is explored for the minimum risk point estimation of the range θ in a power family distribution. This modification of Mukhopadhyay et al.'s (1983) twostage estimation technique is proposed along the lines of Mukhopadhyay and Duggan (1997, 1999) by assuming a prior knowledge of a positive lower bound θL for the otherwise unknown range parameter θ. Expressions for the average sample size and the risk associated with the conventional sample maximum order statistic are investigated. A new estimator of 8 based only on the stopping variable is also investigated. Various second-order asymptotic analyses are supplemented by interesting exact and simulation results.
On Properties and Construction of GEGD ⁄3n -1 PBIB Designs
Authors: Adhikary Basudeb , Bandyopadhyay Sanjoy
Published: August 2016

A definition of subfactor balance is given and it is proved that a necessary and sufficient condition for a design to have subfactor balance is that it is a GEGD⁄3 n-1 PBIB design. Some properties and methods of construction are also studied.
Estimation of the Parameters of Triangular Distribution by Order Statistics
Authors: Samuel Philip , Thomas P. Yageen
Published: August 2016

In this paper, we derive explicit expressions for the single and product moments of order statistics arising from the standard triangular distribution. Best linear unbiased estimators of the location and scale parameters of a triangular distribution based on order statistics are obtained. The efficiencies of these estimators are also compared with estimators based on U-statistics
Identification of Failure Rates
Authors: Gupta R. P. , Gupta R.D. , Sankaran P. G.
Published: August 2016

In this paper, we give an identity based on conditional mean to determine the failure rate of a distribution. Some well-known characterizations are deduced as special cases. We also present various applications of the identity. By extending this to the bivariate case, we obtain a class of distributions with a specified form of failure rate. Finally we study the properties and the applications of the bivariate model.
On the Inter-Relationships Between Some Classes of Life Distributions
Authors: Suresh R. P.
Published: August 2016

It is well lmowu that if F is IFR, theu it is also DM RI; however, the converse is not true, in general. Kupka and Loo (1989) proved that a distribution with convex decreasing mean residual life (CDMRL) function has an Increasing Failure Rate (IFR) distribution. In this paper, we show that this condition (viz., convexity of DMRL) is not nenessary for F to be IF R. It is observed that contrary to the monotonic classes, in the non-monotonic classes, F is BFR does not imply that F is IDMRL. In this paper, we derive a result that gives an additional condition required for a BF R distribution to be an I DM RL distribution.
Inference on P(Y < X) in Generalized Uniform Distributions
Authors: Ali M. Masoom , Pal Manisha , Woo Jungsoo
Published: August 2016

The paper considers estimation and testing of P( Y < X), when X and Y follow independent generalized uniform distributions with known shape parameters .
On a Finite Mixture of Pareto Distributions
Authors: Sankaran P. G. , Nair Maya T.
Published: August 2016

Finite mixtures of probability distributions arise as models of income and wealth in many practical problems. In the present paper, we study the properties of finite mixture of Pareto distributions in the context of income analysis. We develop estimation of the parameters of the finite mixture of Pareto distributions using different methods for complete as well as censored samples. A simulation study and a data analysis are carried out to assess the performance of the estimators.
Mixture Nonlinear Time-Series Analysis : Modelling and Forecasting
Authors: Ghosh Himadri , Sunilkumar G. , Prajneshu
Published: August 2016

Gaussian mixture transition distribution (GMTD) models and mixture autoregressive (MAR) models are generally employed to describe those data sets that depict sudden bursts, outliers and flat stretches at irregular time epochs. In this paper , these two approaches are compared by considering weekly wholesale onion price data during April, 1998 to November, 2001. After eliminating trend, seasonal fluctuations are studied by fitting Box­Jenkins airline model to residual series. To this end, null hypothesis of presence of nonseasonal and seasonal stochastic trends is tested by using Osboru­Chui­Smith­Birchenhall (OCSB) auxiliary regression. Subsequently, appropriate filters in airline model for seasonal fluctuations are selected. Presence of autoregressive co nditional heteroscedasticity (ARCH) is tested by Naive Lagrange multiplier (Nave­ LM) test. Estimation of parameters is carric~d out using Expectation­Maximization (EM) algorithm and the best model is selected on the basis of Bayesian information criterion (BIC). Out­of­sample forecasting is performed for one­step and two­step ahead prediction by uaive approach, proposed by Wong and Li (2000). It is concluded that, for data under consideration, a three­component MAR model performs the best.
An Application of Multivariate Statistical Techniques for Cost Effective Decision Making ­ A Case Study
Authors: Pradhan Biswabrata
Published: August 2016

This paper focuses on the application of multivariate statical techniques for making a cost effective decision in an industrial set up. The objective of this study is to take a decision with respect to several parameters whether a particular product can be sent to the customer or not. The techniques like MANOVA, discriminant and classification function analysis have been used to fulfil the objectives. An optimum classification rule has been established for making the decision. A cost benefit analysis has also been done after iniplementing the proposed optimum decision­making rule.
Some Alternative Methods of Finding the Optimal Order Quantity in Inventory Models
Authors: Chandra Ayan , Mukherjee S. P.
Published: August 2016

We consider a purchase inventory problem where both demand and supply have been taken to be random. Several possible ways of deriving the optimum order quantity based on the distribution of total cost have been proposed. Expressions for the optimum order quantity that minimizes the mode or exceedance probability of this distribution have been worked out for some particular demand and supply distributions.
On the Size Corrected Tests in Improved Estimation
Authors: Hoque Z. , Billah B. , Khan S.
Published: August 2016

In this paper we propose shrinkage preliminary test estimator (SPTE) of the coefficient vector in the multiple linear regression model based on the size corrected Wald ( W), likelihood ratio ( LR) and Lagrangian multiplier ( LM) tests. The correction factors used are those obt,ained from degrees of freedom corrections to the estimate of the error variance and those obtained from the second­order Edgeworth approximations to the exact distributions of the test statistics. The bias and weighted mean squared error (WMSE) fun ctions of the estimators are derived. With respect to WMSE, the relative efficiencies of the SPTEs relative to the maximum likelihood estimator are calculated. This study shows that the amount of conflict can be substantial when the three t ests are based on the same asymptotic chi­square critical value. The conflict among the SPTEs is due to the asymptotic tests not having the correct significance level. The Edgeworth size corrected W, LR and LM tests reduce the conflict remarkably.
Adaptive Allocation Design for Matching Pairs
Authors: Bandyopadhyay Uttam , Mukherjee Shirsendu
Published: August 2016

In the present work , we frame an adaptive allocation rule in matching pairs of experimental units. The proposed rule is a bivariate version of the randomized play the winner (RPvV) rule. We study various properties of the rule through asymptotics and simulations. Related inferential problem is also considered.
Bivariate Weighted Distributions in the Context of Reliability Modelling
Authors: Sunoj S.M. , Sankaran P. G.
Published: August 2016

In this paper we consider the weighted conditional models and bivariate weighted models using different weight functions and examine its relationships in the context of reliability modelling. We also study the dependence nature of the bivariate weighted models using the local dependence function introduced by Holland and Wang (1987).
Bivariate Burr System of Distributions
Authors: Nadh Bismi G. , Nair N. Unnikrishnan , Nair V. K. Ramachandran
Published: August 2016

In the present paper we introduce the bivariate Burr system of distributions by generalizing the differential equation in the univariate case.
Procrustean Strategies for Incompatible Conditional and Marginal Information
Authors: Arnold Barry C.
Published: August 2016

Summary

Full or partial information about the marginals and conditionals of a bivariate distribution is likely to be incompatible. Additionally, information may come from heterogenous sources with limited agreement between sources. Some strategies for selecting a single “minimally incompatible” joint distribution are surveyed.
Estimating Perception of Distance : Applied Sequential Methodologies in Experimental Psychology
Authors: Mukhopadhyay Nitis
Published: August 2016

Summary

An eyewitness's description of a missing criminal, for example, is very crucial for apprehending the individual. But, some accounts may be unreliable if it turned out that the witness was ‘far away’ from a crime scene. Estimation of the perception of “distance” can be an important input in many situations including this one.

We ran a number of designed experiments, collected data, and analyzed them in order to understand how individuals perceived “distance”. These experiments and associated data analyses have some clear messages: When a subject was asked to guess the length of an object such as a straight line or a ruler, we found time and again that one's answer routinely depended upon (i) presence or absence of landmarks or reference points, and (ii) what one had thought that was being shown rather than what the true item really was. More investigations in experimental psychology are deemed essential in one's thorough understauding of human perception of “distance”.
An Extension of the Lack of Memory Property with Characterization Results
Authors: Roy Dilip
Published: August 2016

Summary

In the reliability analysis the lack of memory property plays a pivotal role in conceptualizing some life distribution classes and in unique determination of the exponential distribution. On the other hand quite a few results like constancy of the coefficient of variation of the residual life, linearity of the mean residual life characterize the exponential distribution along with the Lomax distribution. Question that arises is - can there be an extended version of the lack of memory property to tie together the exponential and the Lomax distributions through characterization. The present paper presents an affirmative claim and extends the lack of memory property based on standardization technique. It also presents a stochastic version of this extended property with unique determination of the same life distributions. Attempts have also been made to define this extended lack of memory property in the bivariate set up and indicate the bivariate distributions that satisfy the same.
Detailed Classification Problem
Authors: Banerjee Kaustav
Published: August 2016

Summary

The classification problem is concerned with allocation of new observations on several variables to two or more distinct categories known to exist a priori, on the basis of some pre-solved cases. Most of the existing solutions to the problem lack detailed inference with respect to the outcomes of the concerned random experiment. An alternative procedure is therefore suggested from frequentist viewpoint, involving relative credentials placed on the different candidate groups in terms of betting odds. The underlying theory was introduced in Chatterjee and Chattopadhyay(1993), the present study being an app lication towards the classification problem. Performance of the proposed ruie has been studied for some real-life examples through discriminant analysis.
Exact Density of W Classification Statistic Based on Unmatched Training Sample from Correlated Populations
Authors: Bandyopadhyay Subhadip , Bandyopadhyay Shibdas
Published: August 2016

Summary

A unit is to be classified into one of two correlated homoscedastic normal populations by W classification statistic. The two populations are like two different states of a disease. A sample unit can be observed in both the states (populations) . The observations made on the same unit in the two populations are correlated. W is based on an unmatched training sample where N sample units are observed in both the populations and Ni- N units are observed in population i, i = 1, 2. The exact density of W in such set up is derived for unknown means and common dispersion matrix where the correlation linking the populations is known or unknown. Simulated density of W is plotted and probability of correct classification (PCC) is evaluated using simulation.
Quasi-Empirical Bayes Methods of Estimation in Arma (p, q) Models with Vague Prior Information on MA(q)1
Authors: Haye M. Ould , Saleh A. K. Md. E.
Published: August 2016

This paper investigates the asymptotic properties of various estimators of autocorrelations in an ARMA{p,q) model when vague non-sampling information on the moving average part is available. In particular, we discuss the usual MLE {called unrestricted estimator), restricted MLE (based on vague information), preliminary test estimator, shrinkage estimator and the positive rule estimator of the autocorrelations. It is shown that near the prior information on the MA-parameters, the restricted , preliminary test and shrinkage estimators of the autoregressive parameters perform better than the unrestricted estimator, while their superiority changes as MA-parameters divert from the prior informations. The analysis is based on the asymptotic properties of the estimators under contiguous alternatives.
Optimal Crossover Designs for Comparing Mixed Carryover Effects
Authors: Saharay Rita , Shah Kirti R.
Published: August 2016

In this paper we consider a variant of the traditional noncircular model for crossover designs. Instead of assuming that ea.Ch treatment - applied to an experimental unit imparts the same carryover effect regardless of the treatment applied to the next period on the same unit, we consider the model which assumes two types of carryover effects that extend from a period to the next period. One type is called self carryover effect when a treatment is followed by itself in the next period on the same unit and the other type is called mixed carryover effect when a treatment is followed by any other treatment in the next period. Such models are useful in sensory trials. Efficient estimation and testing of the direct treatment effects (imparted by the treatment itself on the experimental unit of application) as well as the carryover effects under different models are of interest to the practitioners from application and model building point of view and have been addressed by many researchers. In the present article the problem of identification of optimal designs for the estimation of the mixed carryover effects has been taken up. It is shown that under the self and mixed carryover model generalised Patterson's balanced designs (termed also totally balanced designs in the literature}, which are known to be universally optimal for the estimation of the direct treatment effects are also universally optimal for the estimation of the mixed carryover effects provided that the number of periods exceeds two.

AMS (2000} Subject Classification : 62K05.
On Moran's Bivariate Gamma and Bivariate Negative Binomial Distribution
Authors: Jayakumar K. , Mundassery Davis Antony
Published: August 2016

Characterizations of Moran's bivariate gamma distribution and bivariate negative binomial distribution are obtained. Autoregressive models with Moran's bivariate gamma distribution as marginals are developed.
Nonparametric Estimation of Reversed Hazard Rate
Authors: Sankaran P. G. , Gleeja V. L. , Jacob T. M.
Published: August 2016

As hazard function, the role of reversed hazard rate function is well known in reliability analysis. This function is useful in the analysis of left censored lifetime data as well as in the study of parallel systems. In this paper, we discuss nonparametric estimation of reversed hazard rate function for the complete sample as well as for the right­censored observations. Properties of estimators are investigated Performance of the estimators is studied using a simulated data We illustrate the procedures with real data sets.
Bias in Multivariate Generalized Linear Models
Authors: Mukhopadhyay Siuli , Khuri André I.
Published: August 2016

In this article, an expression is derived for the bias associated with maximum likelihood estimates of the parameters in a multivariate generalized linear model (MGLM). This expression represent.s an extension of the bias formula in the case of a univariate generalized linear model. One important objective of the proposed extension is to obtain an expression for the mean squared error of prediction matrix, which can be used as a criterion for comparing response surface designs for a MGLM. An application of the bias formula is presented in the special case of the bivariate binary distribution. A numerical example is given to illustrate this particular application.
On Construction of Pencilwise Orthogonal and Balanced Designs
Authors: Bandyopadhyay S.
Published: August 2016

In this paper some constructions of the Pencilwise Orthogonal and Balanced Designs of Das (2001), mainly based on difference and composition methods, are given.
Analysis of cDNA Microarray Experiment with External Controls : A Mixed Model Approach
Authors: Chen Wei­Chen , Maiti Tapabrata
Published: August 2016

The aim of this article is to obtain the calibration curves by external controls in the cDNA microarray data set. Anonlinear mixed model is found to be suitable for this purpose. The fitted calibration curves could be used to predict the concentrations of the relative expressions by the inverse functions of the fitted curves. After giving some background introduction for a eDNA microarray experiment with external controls, the article focuses on two parts. First, we check the source of experiment variation by using linear model on the slide, dye, and pin effects, and determine the quality of the data set by using quasi­likelihood method for the model with random effect for pins. Second we propose a non­linear model based on a four­parameter logistic function, with two possible random effects structures on pins and base on the concentrations. The inverse function of the fitted model is then used to predict the concentrations from the expression intensities of the external controls.
On Characterizing Distributions VIA Regression on Pairs of Generalized Order Statistics
Authors: Ahsanullah M. , Beg M. I.
Published: August 2016

We present results that lead to characterization of several distributions in terms of the regression of a (possibly non-linear) function of a generalized order statistic with its adjacent generalized order statistics as covariates through the arithmetic, geometric and harmonic means of the functions at the end points.
Characterization of Continuous Distributions by Conditional Variance of Order Statistics
Authors: Khan A. H. , Faizan M. , Khan M. J. S.
Published: August 2016

A generalized family of continuous distributions have been characterized through conditional variance of order statistics. Further, some of its important deductions are also discussed
Some Comments on the Watson Efficiency of the Ordinary Least Squares Estimator Under the Gauss Markov Model
Authors: Puntanen Jaarkko Isotalo Simo , Styan George P. H.
Published: August 2016

We consider the estimation of a given estimable parametric function in the Gauss–Markov model, and focus on questions concerning the Watson efficiency of the ordinary least squares estimator (OLSE) of the given parametric function with respect to the best linear unbiased estimator (BLUE). We apply the Frisch–Waugh–Lovell Theorem for the estimation of the parametric function, and give an interesting decomposition of the total Watson efficiency with respect to the efficiency of the parametric function. Also, a relation between the Watson efficiency of the OLSE of the given parametric function and specific canonical correlations is established.
Hidden Truncation and Additive Components : Two Alternative Skewing Paradigms
Authors: Arnold Barry C. , Gómez Héctor W.
Published: August 2016

The two parameter skew-normal distribution can be viewed as having arisen from a standard normal density by hidden truncation or by an additive component construction. It is of interest to determine whether the two skewing mechanisms can yield the same asymmetric distribution when applied to other symmetric or asymmetric distributions. It is conjectured that the phenomenon only occurs in the normal case. In other cases, hidden truncation and additive components typically lead to different families of skewed distributions. Some examples are provided to illustrate the phenomenon.

AMS (2000) Subject Classification : 60E05, 62E10.
Parametric Estimation of Quality Adjusted Lifetime (QAL) Distribution for two General Illness-Death Models
Authors: Pradhan Biswabrata , Dewanji Anup
Published: August 2016

In this work, we consider the parametric estimation of quality adjusted lifetime (QAL) distribution for two general illness-death models, namely, competing illness-death model and reversible illness-death model. The first model is progressive and involves multiple states, while the second one incorporates possibility of recovery. The main focus of this paper is to derive the theoretical distribution of QAL for the two illness-death models, under some parametric models for the sojourn time distributions in different states. The QAL distribution is then estimated by replacing the parameters in its theoretical expression by the corresponding estimates obtained by using standard survival analysis techniques. The performance of the estimator is investigated through a simulation study.

AMS (2000) Subject Classification : 62N02
Stein Estimation and Prediction : A Synthesis
Authors: Ghosh Malay
Published: August 2016

Stein (1956), in his seminal paper, came with the surprising discovery that the sample mean is an inadmissible estimator of the population mean in three or higher dimensions under squared error loss. The past five decades have witnessed multiple extensions and variations of Stein's results. Extension of Stein's results to prediction problems is of more recent origin, beginning with Komaki (2001) and George et al. (2006) and Ghosh et al. (2006). The present article shows how both the estimation and prediction problems go hand in hand under certain “intrinsic losses”, which includes both the Kullback-Leibler and Bhattacharyya-Hellinger divergence losses. The estimators dominating the sample mean under such losses are motivated both from the Bayesian and empirical Bayes point of view.
Paired Sample Tests with Unordered Observations
Authors: Banerjee Kaustav , Chattopadhyay Gaurangadeb , Banerjee Tathagata
Published: August 2016

The problem of testing equality of means of a bivariate normal distribution on the basis of a sample of size n has been considered when the labels of the observations are not known. Two tests based on the sample moments of absolute values of the differences of the observations in each pair are suggested. Their power properties are investigated. It is interesting to observe that for small values of the parameter one is more powerful than the other while for larger values it is the other way around.

AMS (2000) Subject Classification : 62F03, 62P10.
A Loglikelihood-Based Shape Measure of Past Lifetime Distribution
Authors: Maiti Sudhansu S. , Nanda Asok K.
Published: August 2016

Generalized past information measure based on Rényi entropy for a continuous random variable useful in life testing is considered and its connection to the loglikelihood is established. From this relation, a loglikelihood-based past life distribution measure [Formula: see text] has been proposed. From the gradient of the spectrum of generalized past information, the [Formula: see text] measure has been calculated for some important parametric life distributions. Serving as a measure of the shape of a past life (inactivity time) distribution, [Formula: see text] can be used to compare the tails and shapes of various frequently used densities, where the traditional kurtosis measure is not applicable.
Rate of Convergence in Invariance Principle for Random Partial Sums with Applications
Authors: Dasgupta Ratan
Published: August 2016

Abtsrcat

Under certain assumptions on the random index, an approximation rate in the invariance principle for random partial sums is obtained. As a consequence, two industrial production processes are compared.
A Binary Choice Model with Heterogeneous Errors
Authors: Nadarajah Saralees
Published: August 2016

Abtsrcat

The common assumption with binary choice models is that the errors arise from identical Gumbel distributions. This gives rise to the well known logistic model. In this note, we consider the case when the errors have non—identical Gumbel distributions. We derive explicit expressions for distributional properties of the resulting model, consider estimation issues and illustrate an application to some real data.
On Uncorrelated Linear Functions of Order Statistics of Independent But not Identically Distributed Random Variables
Authors: Sajeevkumar N.K.
Published: August 2016

Abtsrcat

In this paper the correlation between the pooled sample mean and certain linear functions of order statistics of independent non-identically distributed(inid) random variables are obtained for pooled sample from pop- ulations with common location parameter μ and common scale parameter σ and the results if the parent distributions are symmetric about the common location parameter μ are derived therefrom.
Estimation Methods in Evaluation and Design of Reliable Networks: Applications and Scope
Authors: Sharma Megha
Published: August 2016

Abtsrcat

Reliable networks are the ones that take the failure prone nature of network elements into account. They are used to model a wide variety of real life problems. There are two interesting research problems in the area of reliable networks, the problem of quanitfying the network performance in terms of a performance metric, and given a performance metric, the problem of designing a reliable network that meets certain prespecified design criteria. Both of these problems are NP-hard, therefore exact solution methods are of limited use. Real life instances of these problems are solved using Monte Carlo estimation methods. In this paper, we review the various Monte Carlo methods used for estimating the performance of a reliable network and point out directions for future research.
Variable Selection Procedure for Discrimination Between two Multinormal Populations with Common Dispersion Matrix Proportional to a Known Positive Definite Matrix
Authors: Samanta Sisir Kumar
Published: August 2016

Abtsrcat

A stepwise procedure is described for selecting a suitable sub-set of characters for discriminating between two multivariate normal populations with a common dispersion matrix which is an unknown scalar multiple of a known positive denite positive denite matrix. The procedure assumes with a prescribed condence coecient that the distance based on the subset of selected variables is not less than a prescribed proportion of the distance based on all variables. The procedure is consistent in natural sense.
Estimation of Parameters of Uniform Distribution Based on K-Record Values
Authors: M. Shy Mary , Chacko Manoj
Published: August 2016

Abtsrcat

There are many situations where experimental outcomes are a sequence of record-breaking observations. In this paper, an extension of record models, well known as k-records, is considered. The best linear unbiased estimators (BLUEs) for the location and scale parameters of the uniform distribution are derived using k-record values. In addition, best linear invariant estimators of two parameter uniform distribution are obtained on the basis of k-record values. We have also determined the e�ciency of BLUEs relative to maximum likelihood estimators (adjusted for bias). The best linear unbiased predictor of future k-record values is also determined.
Baltic Sea Peracarids Diurnal Activity Data : Issues On Multiple Imputation in Overdispersed Poisson Regression Model and Model Selection
Authors: Harel Ofer , Liu Junfeng , Dey Dipak
Published: August 2016

Abtsrcat

In this paper, we consider the diurnal (day time) activities of peracarisdis in Baltic sea. The peracaridis is a large group of malacostracan crustaceans, having members in marine, freshwater, and terrestrial habitats. They are defined by the possession of a single pair of maxillipeds (rarely 2-3), of mandibles with an articulated accessory process between the molar and incisor teeth in the adults (called the lacinia mobilis), and of a carapace which is often reduced in size and is not fused with the posterior thoracic somites. The experimental data is given in Janson and Kallander (1968). In this study, the animals are caught by sweeping a net over a known distance and fixed time intervals. The total number of caught along with various covariates are recoded. The data is missing some responses and some covariates. In view of that we develop Bayesian approaches for modeling overdispersed Poisson data in the context of regression problem in presence of missing data. We handle the missing data problems through various multiple imputation schemes and take a Bayesian route for model selection to determine the appropriate scheme for the given data.
A Review on Optimum Covariate Designs
Authors: Das Premadhis
Published: August 2016

Study of optimality of designs with covariate models started with Lopes Troya (1982a, 1982b). Later on, it was considered by a number of authors. Notable among them are Das et al. (2003) and Rao et al. (2003). In a series of papers, Dutta, Das and Mandal considered different design set-ups and proposed optimum covariate designs where the covariate effects were estimated with global optimality. The paper contains a short review of the present developments in this connection.
Modifying Classical Randomized Response Techniques with Provision for True Response
Authors: Dihidar Kajal
Published: August 2016

In this paper we consider four well-known randomized response models; the unrelated question model, the unknown repeated trial model, the forced response model and a model for quantitative responses. Traditionally these models are applied to the respondents chosen by simple random sampling with replacement. We show that a modification may be applied to them and irrespective of how a sample is drawn, we may gain in efficiency in estimation. We illustrate our findings through a numerical exercise.
Software Reliability Growth Model Based on Truncated Distributions
Authors: Kantam R. R. L. , Priya M. Ch.
Published: August 2016

Generally a software reliability growth model (SRGM) through a non-homogenous Poisson process (NHPP) is represented by its mean value function originated from the cumulative distribution function of a positive-valued continuous random variable. We consider some truncated distributions of positive-valued random variables and use them in the mean value function of NHPP. The chief characteristics of the resulting SRGMs are presented. Maximum likelihood estimation of parameters is discussed. Reliability aspects of live data sets are evaluated. Relative comparison among the models is also studied.
Means and Variances of Some Statistics in Simple Social Network with Given Out-Degrees
Authors: Jana Rabindranath
Published: August 2016

This study is related to a finite simple social network (SSN), which consists of a finite number of actors of whom any ordered pair either has a dyadic relation or not and has neither multiple arcs nor arcs from the actors to themselves. In this connection different probabilistic models depending on a set of given conditions have been discussed by Rao and Bandyopadhyay (1987). This study is an attempt to find out the means and variances of some statistics which are left undiscussed in an SSN under the probabilistic models as studied by Rao and Bandyopadhyay (1987).
Estimation of the Scale Parameter of Skew-Normal Distribution Using U-Statistics Based on Order Statistics
Authors: Thomas P. Yageen , Baiju K.V.
Published: August 2016

Abtsrcat

In this work, we obtain the best linear unbiased estimator based on order statistics for the scale parameter of skew-normal distribution for some known values of the shape parameter. We also propose a technique for estimating the scale parameter of skew-normal distribution by U-statistics based on best linear functions of order statistics as kernels. The efficiency comparison of the proposed U-statistics with the maximum likelihood esti- mator is also carried out.
Some Symmetry Models for the Analysis of Collapsed Square Contingency Tables with Ordered Categories
Authors: Yamamoto Kouji , Tahata Kouji , Tomizawa Sadao
Published: August 2016

Abtsrcat

For the square contingency tables with ordered categories, there may be some cases that one wants to analyze them by considering collapsed tables with some adjacent categories combined in the original table. This paper considers some symmetry models for collapsed square contingency tables and proposes two new models which have the structure of global symmetry and that of quasi-symmetry for the collapsed square tables. Also this paper gives two kinds of decompositions of the symmetry model for collapsed square tables. The new models and decompositions are useful for analyzing the collapsed square tables. Examples are given.
A Test for Equality of Marginals of Fgm Family of Bivariate Distributions Using Unordered Pairs
Authors: Banerjee Kaustav , Chattopadhyay Gaurangadeb , Banerjee Tathagata
Published: August 2016

Abtsrcat

A test for equality of marginal distributions of Farlie-Gumbel-Morgenstern (FGM) family of bivariate distributions is proposed on the basis of a paired sample of size n, when the labels of the observations are not known. The test has desirable power properties and is an improvement over the test prescribed by Davies and Phillips [1988]. The test is illustrated with some interesting real-life applications.
Two-Stage Estimation Procedure for the Parameter of U (θ,mθ) Distribution
Authors: Patil H.S.
Published: August 2016

Abtsrcat

In the literature, an extensive work on sequential fixed width confidence interval (CI) for the parameter of U(0, θ) model is available. In this article we propose a two-stage fixed width (1 − α) level sequential CI for the parameter θ of U( θ, mθ) distribution, where m > 1 is known, based on the large-sample approximation of coverage probability.
Classification of Encryption Algorithms Using the Hidden Markov Model
Authors: Ray Prabhat Kumar , Kant Shri , Roy Bimal , Basu Ayanendranath
Published: August 2016

Abtsrcat

The “Hidden Markov Model”, HMM for short, represents a very rich class of stochastic models which is extensively used in modeling real data. In particular it has proved to be a strong and powerful tool for classification problems in some specific application areas including speech recognition and image analysis. The model involves a complex stochastic formulation of the underlying process and the implementation is numerically somewhat involved. In this article we present some results involving the application of hidden Markov models in trying to classify a cipher text in terms of the source algorithm generating the cipher when it is known that the source algorithm belongs to a finite list of algorithms. Our specific application is based on ten source algorithms, five each of the stream cipher and block cipher types. We perform a statistical analysis of each cipher text leading to the evaluation of the posterior chances of the cipher being generated by each of the competing source algorithms.

Although there are some other instances of the use of the hidden Markov model in the area of cryptology there is little literature relating to the previous use of this model in the specific context of classification of encryption algorithms, which makes it hard to judge its performance or compare it against an existing standard. However on the basis of our limited study we feel that there is clear indication to suggest that further investigation of the hidden Markov model in the context of classification of encryption algorithms may be worthwhile as they appear to lead to classification results which are clearly better than random assignment.
Designs for Searching two Two-Factor and One Three-Factor Interaction Effect Under the Tree Structure
Authors: Qin Hong , Sarkar Angshuman , Chatterjee Kashinath
Published: August 2016

Abtsrcat

Search designs form an indispensable tool under model uncertainty. However, the progress in this area has been limited due to com- plexities of checking the necessary rank condition for search designs. Designs for searching two two-factor and one three-factor interaction effects under a tree structure in the presence of the general mean and all the main effects are provided here. These designs are obtained under the assumption that four-factor and higher order interaction effects are all absent. Probability of correct searching obtained through simulations is also discussed.
On Nonparametric Estimation of the Density of a Non-Negative Function of Observations
Authors: Chaubey Yogendra P. , Sen Pranab K.
Published: August 2016

Let { X1, ..., X n} be a random sample from a continuous distri- bution F defined on the k−dimensional Euclidean space Rk; for some k≥1. In many statistical applications we are interested in statistical properties of a function h( X1, ..., X m) of m ≥ 1 observations. Frees (1994, J. Amer. Stat. Assoc.) considered estimating the density function g associated with the distribution function

[Formula: see text]

using the kernel method. In many applications, though, the functions of interest are non-negative where the usual symmetric kernels applied in the kernel density estimation are not appropriate. This paper adapts the alter- native density estimator developed in Chaubey and Sen (1996, Statistics and Decisions) by smoothing the so called empirical kernel distribution function:

[Formula: see text]

where 1( A) denotes the indicator of A and [Formula: see text] denotes sum over all possible [Formula: see text] combinations. Applications and asymptotic properties of the alternative estimator are investigated.
Multiple Point Hypothesis Test Problems and Effective Numbers of Tests for Control of the Family-Wise Error Rate
Authors: Dickhaus Thorsten , Stange Jens
Published: August 2016

Abtsrcat

We consider a specific class of multiple test problems, consisting of M simultaneous point hypothesis tests in local statistical experiments. Under certain structural assumptions the global hypothesis contains exactly one element ϑ* (say), and ϑ* is least favourable parameter configuration with respect to the family-wise error rate (FWER) of multiple single-step tests, meaning that the FWER of such tests becomes largest under ϑ*. Further-more, it turns out that concepts of positive dependence are applicable to the involved test statistics in many practically relevant cases, in particular, for multivariate normal and chi-square distributions. Altogether, this allows for a relaxation of the adjustment for multiplicity by making use of the intrinsic correlation structure in the data. We represent product-type bounds for the FWER in terms of a relaxed Šidák-type correction of the overall significance level and compute “effective numbers of tests”. Our methodology can be applied to a variety of simultaneous inference problems for multi-dimensional (location) parameters, as frequently occurring in analysis of variance models or in the context of simultaneous categorical data analysis. For example, simultaneous chi-square tests for association of categorical features are ubiquitous in genetic association studies. In this type of model, Moskvina and Schmidt (2008) gave a formula for an effective number of tests utilizing Pearson's haplotypic correlation coeffcient as a linkage disequilibrium measure. Their result follows as a corollary from our general theory and will be gen- eralized.
Ban Estimates of Class Boundaries Under Likert-Type Scaling
Authors: Bhattacharya Tuhinsubhra , Sengupta Arindam
Published: August 2016

Abtsrcat

We prove that under very mild assumptions, the estimated class boundaries for the method of Likert-type scaling are Best Asymptotic Normal estimators of the true values. Also, we show that in the situation where the number of categories increases with sample size, the estimates are uniformly consistent under suitable conditions.