Journal of Statistical Theory and Applications

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292 articles
Research Article

Kernel Inference on the Generalized Gamma Distribution Based on Generalized Order Statistics

M. Ahsanullah, M. Maswadah, Ali M. Seham
Pages: 152 - 172
The kernel approach has been applied using the adaptive kernel density estimation, to inference on the generalized gamma distribution parameters, based on the generalized order statistics (GOS). For measuring the performance of this approach comparing to the Asymptotic Maximum likelihood estimation,...
Research Article

Tail dependence of perturbed copulas

Jozef Komorník, Magda Komorníková, Jana Kalická, Cuong Nguyen
Pages: 153 - 160
In this paper, we extend our investigations of a special class of perturbations of copulas introduced in [7]. Despite a surprising fact that this kind of perturbations does not change the value of tail dependence of the original copulas, their use yielded models with considerably improved fitting qualities.
Research Article

A Generalization of the Sukhatme's Test for Two-Sample Scale Problem

Manish Goyal, Narinder Kumar
Pages: 155 - 170
In this paper, we present nonparametric tests for the two-sample scale problem. The proposed tests include as special case the B.V. Sukhatme, Ann. Math. Stat. 28 (1957), 188–194, and J.V. Deshpande, K. Kusum, Aust. J. Stat. 26 (1984), 16–24 tests. The asymptotic distribution of the test statistics is...
Research Article

Bayesian test of independence and conditional independence of two ordinal variables

Zahra Saberi, Mojtab Ganjali
Pages: 156 - 168
For analysis of contingency tables with large sample size, classical approaches using approximate methods have high power. However, when the sample size is small or some cells have frequencies less than 5, classical approaches are so conservative. Also asymptotic behavior may be poor when the table contains...
Research Article

Divergence Measures Estimation and Its Asymptotic Normality Theory Using Wavelets Empirical Processes I

Amadou Diadié Ba, Gane Samb LO, Diam Ba
Pages: 158 - 171
We deal with the normality asymptotic theory of empirical divergences measures based on wavelets in a series of three papers. In this first paper, we provide the asymptotic theory of the general of ϕ-divergences measures, which includes the most common divergence measures : Renyi and Tsallis families...
Research Article

Testing EBU_mgf Class of Life Distributions based on Goodness of Fit approach

A.M. Gadallah
Pages: 161 - 168
Based on the goodness of fit approach, a new test is presented for testing exponentiality against "exponential Better than Used in moment generating function ordering class" (EBUmgf). The critical values and the powers of this test are calculated. It is shown that the proposed test...
Research Article

Moments of Progressive Type-II Right Censored Order Statistics from a General Class of Doubly Truncated Continuous Distributions

Jagdish Saran, Narinder Pushkarna
Pages: 162 - 174
In this paper we derive some general recurrence relations between moments of progressively Type-II right censored order statistics from a general class of doubly truncated distributions, thus unifying the earlier results in this direction due to several authors.
Research Article

An Extension of Generalized Cumulative Residual Entropy

Saeid Tahmasebi, Maryam Eskandarzadeh, Ali Akbar Jafari
Pages: 165 - 177
In this paper, a new extension of cumulative residual entropy is proposed. It contain the generalized cumulative residual entropy introduced by Psarrakos and Navarro (2013) and is related with the k-record values. We also consider a dynamic version of this new cumulative residual entropy using the residual...
Research Article

On the Weibull-X family of distributions

Ayman Alzaatreh, Indranil Ghosh
Pages: 169 - 183
In this paper, the Weibull-X family is proposed and some of its properties are discussed. A member of the Weibull-X family, the Weibull-logistic distribution, is defined and studied. Various properties of the Weibulllogistic distribution are obtained. The distribution is found to be unimodal and the...
Research Article

Exponential-Discrete Generalized Exponential Distribution: A New Compound Model

Vahid Nekoukhou, Hamid Bidram
Pages: 169 - 180
In this paper, the researchers attempt to introduce a new generalization of the exponential distribution. This new model is obtained by compounding the exponential distribution and discrete generalized exponential distribution of a second type, which is a generalization of the geometric distribution....
Research Article

Recurrence Relations for Moments and Estimation of Parameters of Extended Exponential Distribution Based on Progressive Type-II Right-Censored Order Statistics

Devendra Kumar, Mansoor Rashid Malik, Sanku Dey, Muhammad Qaiser Shahbaz
Pages: 171 - 181
In this article we derive the recurrence relations for the single and product moments based on progressively Type-II right-censored order statistics for the extended exponential (EE) distribution. The estimation of the model parameters under progressively Type-II right-censored order statistics are obtained...
Research Article

On Some Aspects of Strong Risk Class and Associated Ordering

Mervat Mahdy
Pages: 172 - 192
The paper opens up a new aging class and a new stochastic orders which is depend on risk class, that plays vital role in the reliability theory, finance topics, stochastic orders, and the economic theory. The article presents some new interesting implications and characterizations concerning this class....
Research Article

On Approximating the Distribution of Quadratic Forms in Gamma Random Variables and Exponential Order Statistics

A. Akbar Mohsenipour, Serge B. Provost
Pages: 173 - 184
This paper proposes a moment-based approximation to the distribution of quadratic forms in gamma random variables. Quadratic forms in order statistics from an exponential population are considered as well. Actually,several test statistics can be expressed in terms of the latter. The density approximants...
Research Article

Bayesian Analysis of Misclassified Generalized Power Series Distributions Under Different Loss Functions

Peer Bilal Ahmad
Pages: 173 - 184
In certain experimental investigations involving discrete distributions external factors may induce measurement error in the form of misclassification. For instance, a situation may arise where certain values are erroneously reported; such a situation termed as modified or misclassified has been studied...
Research Article

Bayesian Inference for Exponential Lifetime Models Based on Type-II Hybrid Censoring

Husam Awni Bayoud
Pages: 175 - 188
This article deals with the problem of estimating the parameters of the two-parameter exponential lifetime distribution based on Type-II hybrid censored samples from the Bayesian viewpoint. The scale and location parameters are assumed to have exponential and uniform priors respectively. Bayes point...
Research Article

Statistical Inference for Lindley Model based on Type II Censored Data

A. Asgharzadeh, H.K.T. Ng, R. Valiollahi, M. Azizpour
Pages: 178 - 197
In this paper, the moment-based, maximum likelihood and Bayes estimators for the unknown parameter of the Lindley model based on Type II censored data are discussed. The expectation maximization (EM) algorithm and direct maximization methods are used to obtained the maximum likelihood estimator (MLE)....
Research Article

Estimating the parameter of Exponential distribution under Type-II censoring from fuzzy data

Nayereh Bagheri Khoolenjani, Fateme Shahsanaie
Pages: 181 - 195
Statistical analysis of lifetime distributions under Type-II censoring scheme is based on precise lifetime data. However, in real situations all observations and measurements of Type-II censoring scheme are not precise numbers but more or less non-precise, also called fuzzy. This paper deals with the...
Research Article

Gaussian Copula–based Regression Models for the Analysis of Mixed Outcomes: An Application on Household's Utilization of Health Services Data

Z. Rezaei Ghahroodi, R. Aliakbari Saba, T. Baghfalaki
Pages: 182 - 197
In analyzing most correlated outcomes, the popular multivariate Gaussian distribution is very restrictive and therefore dependence modeling using copulas is nowadays very common to take into account the association among mixed outcomes. In this paper, we use Gaussian copula to construct a joint distribution...
Research Article

Expectation Identities of Generalized Order Statistics from Marshall-Olkin Extended Uniform Distribution and its Characterization

Haseeb Athar, Nayabuddin
Pages: 184 - 191
The Marshall-Olkin extended uniform distribution is introduced and studied by Jose and Krishna (2011). In this paper some moments properties of generalized order statistics (gos) for this distribution are investigated and results are deduced for order statistics and record values. In the last section,...
Research Article

Generalized Chain Exponential-Type Estimators under Stratified Two-Phase Sampling with Subsampling the Nonrespondents

Aamir Sanaullah, Muhammad Hanif
Pages: 185 - 195
In this paper some generalized exponential-type chain estimators have been proposed for the finite population mean in the presence of nonresponse under stratified two-phase sampling when mean of another auxiliary variable is readily available. The expressions for the bias and mean square error of proposed...
Research Article

Testing the mean of an exponential distribution in the presence of outliers

Abbas Mahdavi
Pages: 185 - 190
In this study, we propose a simple robust test for the mean of an exponential distribution by using the simplified version of “Forward Search” (FS) method. The FS method is a powerful general method for identifying outliers and their effects on inferences about the hypothesized model. The simulation...
Research Article

Comparisons of Mixed Systems Using Mean Vitality Function

A. Toomaj, Doostparast M.
Pages: 189 - 195
The concept of system signature is widely used for comparing of mixed (coherent) systems. In practical situa- tions, it is usually impossible to compare mixed systems. To do this, some partial orders are considered in the literature. In this paper, we define a new concept of stochastic order for comparing...
Research Article

Bayesian Test of Homogeneity in Transition Model for Longitudinal Ordinal Response Data with Missing Values

S. Noorian, M. Ganjali
Pages: 191 - 199
For analyzing longitudinal ordinal response data, many methods are available to take into account the correlations between responses of the same individual where different methods use different approaches. One of the methods to consider this correlation is the transition (Markov) model. In this paper,...
Research Article

Estimating Per Capita Rates Using Aggregate Measurements From Groups of Diverse Compositions

Donald N. Stengel, Priscilla Chaffe-Stengel
Pages: 192 - 203
This paper considers the problem of estimating a variable mean for a population of elements where data are only available as aggregate sums for groups of multiple elements. The proposed model addresses an additional complication created when the group measure includes the contribution of diverse elements...
Review Article

On Evolution of Statistical Inference

DAS Fraser
Pages: 193 - 205
The foundations of statistics have evolved over many centuries, perhaps millennia, with major paradigm shifts of the form described in Kuhn (1962). We briefly consider these important transitions and how they have led to major shifts in the foundations of statistical inference. Clearly there is no conventional...
Research Article

A note on the Fisher information matrix of the Birnbaum–Saunders distribution

Artur J. Lemonte
Pages: 196 - 205
We show that the Fisher information matrix of the Birnbaum–Saunders distribution can present numerical problems for some values of the shape parameter. To overcome this problem, we provide a simple analytical approximation which works very well.
Research Article

Estimation under a finite mixture of modified Weibull distributions based on censored data via EM algorithm with application

Saieed F. Ateya, Amirah S. Alharthi
Pages: 196 - 204
In this paper, the maximum likelihood estimates (MLE's) of the parameters of a finite mixture of modified Weibull (MW (alpha, beta, gamma)) distributions are obtained based on type-I and type-II censored samples using the EM algorithm. A simulation study is carried out to study the behavior of the mean...
Research Article

A 3-Component Mixture of Exponential Distribution Assuming Doubly Censored Data: Properties and Bayesian Estimation

Muhammad Tahir, Muhammad Aslam, Muhammad Abid, Sajid Ali, Mohammad Ahsanullah
Pages: 197 - 211
The output of an engineering process is the result of several inputs, which may be homogeneous or heterogeneous and to study them, we need a model which should be flexible enough to summarize efficiently the nature of such processes. As compared to simple models, mixture models of underlying lifetime...
Research Article

A New Bivariate Distribution Obtained by Compounding the Bivariate Normal and Geometric Distributions

Eisa Mahmoudi, Hamed Mahmoodian
Pages: 198 - 208
Recently, Mahmoudi and Mahmoodian [7] introduced a new class of distributions which contains univariate normal–geometric distribution as a special case. This class of distributions are very flexible and can be used quite effectively to analyze skewed data. In this paper we propose a new bivariate distribution...
Research Article

Bivariate and Multivariate Weighted Kumaraswamy Distributions: Theory and Applications

Indranil Ghosh
Pages: 198 - 211
Weighted distributions (univariate and bivariate) have received widespread attention over the last two decades because of their flexibility for analyzing skewed data. In this paper, we derive the bivariate and multivariate weighted Kumaraswamy distributions via the construction method as discussed in...
Research Article

A Measure of Inaccuracy in Order Statistics

Richa Thapliyal, H.C. Taneja
Pages: 200 - 207
In this article, we consider a measure of inaccuracy between distributions of the i-th order statistics and parent random variable. It is shown that the inaccuracy measure characterizes the distribution function of parent random variable uniquely. We also discuss some properties of the proposed measure.
Research Article

Shrinkage estimates for multi-level heteroscedastic hierarchical normal linear models

S.K. Ghoreishi, A. Mostafavinia
Pages: 204 - 213
Empirical Bayes approach is an attractive method for estimating hyperparameters in hierarchical models. But, under the assumption of normality for a multi-level heteroscedastic hierarchical model, which involves several explanatory variables, the analyst may often wonder whether the shrinkage estimators...
Research Article

Some Inferences on the Levy distribution

M. Ahsanullah, Valery B. Nevzorov
Pages: 205 - 211
Some distributional properties of Levy distribution are presented. Limiting distributions of the extreme order statistics are given. Based on the distributional properties a characterization of the Levy distribution is shown.
Letter to Editor

Letter to the Editor

Miroslav M. Ristić
Pages: 206 - 206
Research Article

Record Ranges for Samples From Asymmetrical Laplace Distributions

I.V. BELKOV, M. AHSANULLAH, V. B. NEVZOROV
Pages: 206 - 212
The representations of record ranges via sums of independent identically distributed exponential random variables are obtained for asymmetrical Laplace distributions. This result generalizes the corresponding relations for record values in the cases of exponential and negative exponential distributions
Research Article

Some Inferences on Semicircular Distribution

M. Ahsanullah
Pages: 207 - 213
Several distributional properties of semicircular distribution are presented. The limiting distributions of the standardized extreme order statistics are given. Some characterizations of the distribution are shown.
Review Article

On a Comparison of Tests of Homogeneity of Binomial Proportions

Martin Klein, Peter Linton
Pages: 208 - 224
There are multiple tests of homogeneity of binomial proportions in the statistics literature. However, when working with sparse data, most test procedures may fail to perform well. In this article we review nine classical and recent testing procedures, including the standard Pearson and likelihood ratio...
Research Article

Comparing Two MLEs of The Change Point When an X̄ Control Chart Is Used

Mohammad E. Dehghan Monfared, Fazlollah Lak
Pages: 209 - 218
To find the change point of a normal process monitored by an X control chart, the first and most important step is to find a good estimate of the change point. Different from all the previous studies in which the MLE of the change point is computed...
Research Article

Simultaneous Optimization of Multiple Responses That Involve Correlated Continuous and Ordinal Responses According to the Gaussian Copula Models

Fatemeh Jiryaie, Ahmad Khodadadi
Pages: 212 - 221
This study investigates the simultaneous optimization of multiple correlated responses that involve mixed ordinal and continuous responses. The proposed approach is applicable for responses that have either an all ordinal categorical form are continuous but have different marginal distributions, or when...
Research Article

Augmented Strength Reliability of Equipment Under Gamma Distribution

N. Chandra, Subhradev Sen
Pages: 212 - 221
The strength-reliability of equipment is defined as the probability that the strength of the equipment exceeds its stress. Augmentation of strength-reliability of equipments gives better service protection and longevity. In this paper, the concept of Augmentation Strategy Plan (ASP) is introduced under...
Research Article

Measure of Departure from Marginal Homogeneity for the Analysis of Collapsed Square Contingency Tables with Ordered Categories

Kouji Yamamoto, Itsumi Iwama, Sadao Tomizawa
Pages: 212 - 222
For square contingency tables with ordered categories, there would be some situations that one would like to analyze them by using collapsed 3×3 tables combining some adjacent categories in the original table. This paper considers the marginal homogeneity for collapsed tables and proposes a measure which...
Research Article

The Extended Exponential Distribution and Its Applications

Ahmed Z. Afify, Mohamed Zayed, Mohammad Ahsanullah
Pages: 213 - 229
We introduce a new three-parameter extension of the exponential distribution called the odd exponentiated half-logistic exponential distribution. Various of its properties including quantile and generating functions, ordinary and incomplete moments, mean residual life, mean inactivity time and some characterizations...
Research Article

RKHS approach for signal detection in rotation and scale space random fields

K. Shafie, Akbar Abravesh
Pages: 214 - 220
Two important papers of Worsley, Siegmund and coworkers consider rotation and scale space random fields for detecting signals in fMRI (functional magnetic resonance imaging) brain images. They use the global maxima of images for detection of a signal. In the current work, we utilize a reproducing kernel...
Research Article

Study of Dual to Ratio-Cum-Product Estimator of Finite Population Mean under Double Sampling in Sample Surveys

Sanjib Choudhury, Bhupendra Kumar Singh
Pages: 214 - 221
A class of estimator based on dual to ratio and dual to product-type estimator in double sampling for estimating finite population mean is proposed. The bias and mean square error of the proposed estimator are obtained in two different cases. A comparative study has been made with usual estimators, dual...
Research Article

Stochastic Comparisons of Extreme Order Statistics in the Heterogeneous Exponentiated Scale Model

Esmaeil Bashkar, Hamzeh Torabi, Rasool Roozegar
Pages: 219 - 238
The effect of heterogeneity on order statistics has attracted much attention in recent decades. In this paper, first, we discuss stochastic comparisons of extreme order statistics from independent heterogeneous exponentiated scale samples. These comparisons are made with respect to usual stochastic,...
Research Article

Missing Value Imputation for RNA-Sequencing Data Using Statistical Models: A Comparative Study

Taban Baghfalaki, Mojtaba Ganjali, Damon Berridge
Pages: 221 - 236
RNA-seq technology has been widely used as an alternative approach to traditional microarrays in transcript analysis. Sometimes gene expression by sequencing, which generates RNA-seq data set, may have missing read counts. These missing values can adversely affect downstream analyses. Most of the methods...
Research Article

Characterizations of a Class of Distributions by Dual Generalized Order Statistics and Truncated Moments

Filippo Domma, G.G. Hamedani
Pages: 222 - 234
The problem of characterizing a distribution is an important problem which has recently attracted the attention of many researchers. Thus, various characterizations have been established in many different directions. The present work deals with the characterizations of a general class of distributions....
Research Article

The Kumaraswamy-G Poisson Family of Distributions

Manoel Wallace A. Ramos, Pedro Rafael D. Marinho, Gauss M. Cordeiro, Ronaldo V. da Silva, G.G. Hamedani, Joao Pessoa
Pages: 222 - 239
For any baseline continuous G distribution, we propose a new generalized family called the Kumaraswamy-G Poisson (denoted with the prefix “Kw-GP”) with three extra positive parameters. Some special distributions in the new family such as the Kw-Weibull Poisson, Kw-gamma Poisson and Kw-beta Poisson distributions...
Research Article

Bounded Risk Estimation of the Gamma Scale Parameter in a Purely Sequential Sampling Procedure

Eisa Mahmoudi, Ghahraman Roughani, Ashkan Khalifeh
Pages: 222 - 235
We consider the purely sequential procedure for estimating the scale parameter of a gamma distribution with known shape parameter, when the risk function is bounded by the known preassigned number. In this paper, we provide asymptotic formulas for the expectation of the total sample size. Also, we propose...
Research Article

Marshall–Olkin Power Generalized Weibull Distribution with Applications in Engineering and Medicine

Ahmed Z. Afify, Devendra Kumar, I. Elbatal
Pages: 223 - 237
This paper proposes a new flexible four-parameter model called Marshall–Olkin power generalized Weibull (MOPGW) distribution which provides symmetrical, reversed-J shaped, left-skewed and right-skewed densities, and bathtub, unimodal, increasing, constant, decreasing, J shaped, and reversed-J shaped...