Journal of Statistical Theory and Applications

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262 articles

BAYESIAN APPROACH IN ESTIMATION OF SHAPE PARAMETER OF THE EXPONENTIATED MOMENT EXPONENTIAL DISTRIBUTION

Kawsar Fatima, S.P Ahmad*
Pages: 359 - 374
In this paper, Bayes estimators of the unknown shape parameter of the exponentiated moment exponential distribution (EMED)have been derived by using two informative (gamma and chi-square) priors and two non-informative (Jeffrey’s and uniform) priors under different loss functions, namely, Squared Error...

Two New Lifetime Distributions of X–Weibull Family: Theories and Applications

Abouzar Bazyari, Monjed H. M. Samuh
Pages: 375 - 392
In this paper, two new distributions, weibull-rayleigh and weibull-exponential of X–weibull family are introduced. The various properties of theses distributions, for example, the density functions, distribution functions, hazard rate functions, moment functions and Shannon entropy are investigated and...

On the Characterizations of Chen’s Two-Parameter Exponential Power Life-Testing Distribution

M. Shakil, M. Ahsanullah, B. M. Golam Kibria
Pages: 393 - 407
Characterizations of probability distributions play important roles in probability and statistics. Before a particular probability distribution model is applied to fit the real world data, it is essential to confirm whether the given probability distribution satisfies the underlying requirements by its...

Characterizations of Exponential Distribution Based on Two-Sided Random Shifts

Santanu Chakraborty, George P. Yanev
Pages: 408 - 418
A new characterization of the exponential distribution is obtained. It is based on an equation involving randomly shifted (translated) order statistics. No specific distribution is assumed for the shift random variables. The proof uses a recently developed technique including the Maclaurin series expansion...

Shannon Information in K-records for Pareto-type Distributions

Zohreh Zamani, Mohsen Madadi
Pages: 419 - 438
Pareto distributions provides models for many applications in the social, natural and physical sciences. In this paper, we derive the Shannon information contained in upper (lower) k-record values and associated k-record times of Pareto-type distributions for a finite sample of fixed size and for an...

Parameter Estimation Using the EM Algorithm for Symmetric Stable Random Variables and Sub-Gaussian Random Vectors

Mahdi Teimouri, Saeid Rezakhah, Adel Mohammadpour
Pages: 439 - 461
Applying some well-known properties of the class of symmetric α-stable (SαS) distribution, the EM algorithm is extended to estimate the parameters of SαS distributions. Furthermore, we extend this algorithm to the multivariate sub-Gaussian α-stable distributions. Some comparative studies are performed...

Active and Dynamic Approaches for Clustering Time Dependent Information: Lag Target Time Series Clustering and Multi-Factor Time Series Clustering

Doo Young Kim, Chris P. Tsokos
Pages: 462 - 477
One of data mining schemes in statistics is clustering panel data such as longitudinal data and time series data. Classical approaches to cluster such time dependent information do not properly count time dependencies among objects we are interested to analyze. In the present study, we propose an approach...

Generalized Poisson and Geometric Distributions – An Alternative Approach

Md. Tareq Ferdous Khan, Mian Arif Shams Adnan, Md. Forhad Hossain, Abdullah Albalawi
Pages: 478 - 490
An alternative approach of Poisson and Geometric distributions having a more general form of sampling method are suggested in this paper and defined them as generalized Poisson and generalized Geometric distributions respectively. It is evident that the traditional forms of both the distributions are...

Parameter Estimation and Application of Generalized Inflated Geometric Distribution

Avishek Mallick, Ram Joshi
Pages: 491 - 519
A count data that have excess number of zeros, ones, twos or threes are commonplace in experimental studies. But these inflated frequencies at particular counts may lead to overdispersion and thus may cause difficulty in data analysis. So to get appropriate results from them and to overcome the possible...

f-Majorization with Applications to Stochastic Comparison of Extreme Order Statistics

Esmaeil Bashkar, Hamzeh Torabi, Ali Dolati, Félix Belzunce
Pages: 520 - 536
In this paper, we use a new partial order, called f-majorization order. The new order includes as special cases the majorization, the reciprocal majorization and the p-larger orders. We provide a comprehensive account of the mathematical properties of the f-majorization order and give applications of...

Estimating the Parameters of a Generalized Exponential Distribution

Syed Afzal Hossain
Pages: 537 - 553
A three-parameter generalized exponential distribution was suggested by Hossain and Ahsanullah [5]. Some important aspects of this distribution in the area of estimation remain unexplored in the earlier works. We discuss here the maximum likelihood (ML) method and the method of moments to estimate the...

The Exponential Lindley Odd Log-Logistic-G Family: Properties, Characterizations and Applications

Mustafa Ç. Korkmaz, Haitham M. Yousof, G. G. Hamedani
Pages: 554 - 571
A new family of distributions called the exponential Lindley odd log-logistic G family is introduced and studied. The new generator generalizes three newly defined G families and also defines two new G families. We provide some mathematical properties of the new family. Characterizations based on truncated...

Modeling Pinhole Phenomenon in Sanitary Porcelains Case Study: Isatis Sanitary Porcelain Plant, Yazd, Iran

H. Bazargan, A. Dehghanzadeh
Pages: 572 - 586
Sanitary porcelain products might have several defects, causing potential high-grade desirable products be converted into low-grade ones. Some of the defects are such that a few of them in the products will result in a great fall of product rating and consequently reduction of its value and price. Among...

On Time Series Analysis for Repeated Surveys

Mohamed A. Ismail, Hend A. Auda, Yehia Ahmed Elzafrany
Pages: 587 - 596
Governments and other agencies repeated many important surveys at regular time intervals, but the population mean is estimated mainly using the latest survey. Time series estimators for the population mean using repeated surveys are superior to those obtained from the last survey. This superiority may...

Estimation of a Finite Population Proportion in Light of Randomized Reporting

Pulakesh Maiti, Jyotirmoy Sarkar, Bikas K. Sinha
Pages: 597 - 605
In large scale surveys, it is customary to accept unaltered the responses provided by the respondents, leaving no provision for investigators to pass on any circumstantial judgment on the responses. This restrictive practice sometimes vitiates the estimation of a parameter. Here we consider a real life...

A Study of the First-Order Continuous-Time Bilinear Processes Driven by Fractional Brownian Motion

Abdelouahab Bibi, Fateh Merahi
Pages: 606 - 615
The continuous-time bilinear (COBL) process has been used to model non linear and/or non Gaussian datasets. In this paper, the first-order continuous-time bilinear COBL (1, 1) model driven by a fractional Brownian motion (fBm for short) process is presented. The use of fBm processes with certain Hurst...

A Generalized Class of Estimators for Estimating Population Mean in the Presence of Non-Response

Iram Saleem, Aamir Sanaullah, Muhammad Hanif
Pages: 616 - 626
Koyuncu and Kadilar proposed an estimator based on single auxiliary variable with complete response in stratified random sampling. In this paper, we extended Koyuncu and Kadilar’s estimator to a more generalized class of estimators using two auxiliary variables in stratified random sampling for the situation...

Interval-Valued Uncertainty Based on Entropy and Dempster–Shafer Theory

F. Khalaj, E. Pasha, R. Tavakkoli-Moghaddam, M. Khalaj
Pages: 627 - 635
This paper presents a new structure as a simple method at two uncertainties (i.e., aleatory and epistemic) that result from variabilities inherent in nature and a lack of knowledge. Aleatory and epistemic uncertainties use the concept of the entropy and Dempster–Shafer (D–S) theory, respectively. Accordingly,...

Efficient Estimator of Parameters of a Multivariate Geometric Distribution

U. J. Dixit, S. Annapurna
Pages: 636 - 646
The maximum likelihood estimator (MLE) and uniformly minimum variance unbiased estimator (UMVUE) for the parameters of a multivariate geometric distribution (MGD) have been derived. A modification of the MLE estimator (modified MLE) has been derived in which case the bias is reduced. The mean square...

A Comprehensive Study on Power of Tests for Normality

Hadi Alizadeh Noughabi
Pages: 647 - 660
Many statistical procedures assume that the underling distribution is normal. In this paper, we consider the popular and powerful tests for normality and investigate the power values of these tests to detect deviations from normality. The family of fourparameter generalized lambda distributions (FMKL)...

Bayesian Premium Estimators for Mixture of Two Gamma Distributions Under Squared Error, Entropy and Linex Loss Functions: With Informative and Non Informative Priors

Fatma Zohra Attoui, Halim Zeghdoudi, Ahmed Saadoun
Pages: 661 - 673
In this paper, we consider the Zeghdoudi distribution as the conditional distribution of Xn | 𝜃, we focus on estimation of the Bayesian premium under three loss functions (squared error which is symmetric, Linex and entropy, which are asymmetric), using non-informative and informative priors (the extension...

On Properties and Applications of a Two-Parameter Xgamma Distribution

Subhradev Sen, N. Chandra, Sudhansu S. Maiti
Pages: 674 - 685
An existing one-parameter probability distribution can be very well generalized by adding an extra parameter in it and, in turn, the two-parameter family of distributions, thus obtained, provides added flexibility in modeling real life data. In this article, we propose and study a two-parameter generalization...

On the Lindley Record Values and Associated Inference

A. Fallah, A. Asgharzadeh, S.M.T.K. MirMostafaee
Pages: 686 - 702
In this paper, we discuss the record values arising from the Lindley distribution. We compute the means, variances and covariances of the record values. These values are used to compute the best linear unbiased estimators (BLUEs) and the best linear invariant estimators (BLIEs) of the location and scale...

Weighted Entropy Measure: A New Measure of Information with ts Properties in Reliability Theory and Stochastic Orders

M. Mahdy
Pages: 703 - 718
The weighted entropy measure is a germane dynamic measure of uncertainty in reliability and survival studies. In this paper, the new results of weighted entropies with some characterizations are provided. Furthermore, we have presented some results for weighted entropy residual and weighted past residual...

Weibull-Normal Distribution and its Applications

Felix Famoye, Eno Akarawak, Matthew Ekum
Pages: 719 - 727
In this paper, a Weibull-normal distribution, based on the standard quantile function of log-logistic distribution, is defined and studied. Some properties of the probability distribution are discussed. The Weibull-normal distribution is found to be unimodal or bimodal. The distribution can be right...

A New Zero-Truncated Version of the Poisson Burr XII Distribution: Characterizations and Properties

Haitham M. Yousof, Mohammad Ahsanullah, Mohamed G. Khalil
Pages: 1 - 11
In this work, a new four-parameter zero-truncated Poisson Topp Leone Burr XII distribution is defined and studied. Various structural mathematical properties of the proposed model including ordinary and incomplete moments, residual and reversed residual life functions, generating functions, order statistics...

A Family of Ratio Estimators in Stratified Random Sampling Utilizing Auxiliary Attribute Along Side the Nonresponse Issue

Usman Shahzad, Muhammad Hanif, Nursel Koyuncu, A. V. Garcia Luengo
Pages: 12 - 25
This article proposes some estimators based on an adaptation of the estimators developed by Bahl and Tuteja [1], Diana [2], Koyuncu and Kadilar [3], Koyuncu and Kadilar [4], Shabbir and Gupta [5], and Koyuncu [6] utilizing available supplementry attributes. Further, a new family of estimators is also...

Discrete Additive Weibull Geometric Distribution

K. Jayakumar, M. Girish Babu
Pages: 33 - 45
Discretizing a continuous distribution has received much attention among researchers recently. Discrete analogue of the well-known continuous distributions such as Normal, Exponential, Weibull, Laplace, Rayleigh, and so on, are available in the literature. In this paper, we introduce a discrete version...

Statistical Inference for Topp–Leone-generated Family of Distributions Based on Records

Mohd Arshad, Qazi Azhad Jamal
Pages: 65 - 78
In this paper, we consider a general family of distributions generated by Topp–Leone distribution (known as TL family of distributions) proposed by Rezaei et al. [1]. We consider the problem of estimation of the shape parameter, scale parameter, and reliability function based on record data from TL family...

Bayes and Non-Bayes Estimation of Change Point in Nonstandard Mixture Inverse Weibull Distribution

Masoud Ganji, Roghayeh Mostafayi
Pages: 79 - 86
We consider a sequence of independent random variables X1,X2,…,Xm,…,Xnn≥3 exhibiting a change in the probability distribution of the data generating mechanism. We suppose that the distribution changes at some point, called a change point, to a second distribution for the remaining observations. We propose...

Interval Estimation of the Overlapping Coefficient of Two Exponential Distributions

Sibil Jose, Seemon Thomas, Thomas Mathew
Pages: 26 - 32
For the overlapping coefficient between two one-parameter or two-parameter exponential distributions, confidence intervals are developed using generalized pivotal quantities. The accuracy of the proposed solutions are assessed using estimated coverage probabilities, and are also compared with other approximate...

On Partially Linear Single-Index Models with Missing Response and Error-in-Variable Predictors

Tsung-Lin Cheng, Yin-Ying Lin, Xuewen Lu, Radhey Singh
Pages: 46 - 64
In this paper, we consider a partially linear single-index model when missing responses and nonlinear regressors with measurement error are taken into account. Utilizing data imputation for missing values and regression calibration for error-prone regressors, we not only estimate the parameters in the...

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

Amadou Diadié Bâ, Gane Samb Lo, Diam Bâ
Pages: 113 - 122
In the two previous papers of this series, the main results on the asymptotic behaviors of empirical divergence measures based on wavelets theory have been established and particularized for important families of divergence measures like Rényi and Tsallis families and for the Kullback-Leibler measures....

Generalized Order Statistics from Marshall–Olkin Extended Exponential Distribution

Haseeb Athar, Nayabuddin, Saima Zarrin
Pages: 129 - 135
A.W. Marshall, I. Olkin, Biometrika. 84 (1997), 641–652, introduced an interesting method of adding a new parameter to an existing distribution. The resulting new distribution is called as Marshall–Olkin extended distribution. In this paper some recurrence relations for marginal and joint moment generating...

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...

The LINEX Weighted k-Means Clustering

Narges Ahmadzadehgoli, Adel Mohammadpour, Mohammad Hassan Behzadi
Pages: 147 - 154
LINEX weighted k-means is a version of weighted k-means clustering, which computes the weights of features in each cluster automatically. Determining which entity is belonged to which cluster depends on the cluster centers. In this study, the asymmetric LINEX loss function is used to compute the dissimilarity...

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...

Tests on a Subset of Regression Parameters for Factorial Experimental Data with Uncertain Higher Order Interactions

Shahjahan Khan, Budi Pratikno, Shafiqur Rahman, M. Zakir Hossain
Pages: 103 - 112
The data generated by many factorial experiments are analyzed by linear regression models. Often the higher order interaction terms of such models are negligible (e.g., R. Mead, The Design of Experiments, Cambridge University Press, Cambridge, 1988, p. 368) although there is uncertainty around it. This...

Some Characterization Results Based on the Mean Vitality Function of the First-Order Statistics

A. Toomaj, A. Shirvani
Pages: 123 - 128
In this paper, we investigate some new properties of the mean vitality function (MVF) of a random variable, proposed by A. Toomaj, M. Doostparast, J. Stat. Theory Appl. 13 (2013), 189–195. Specifically, we explore properties of MVF and study under what conditions the MVF of the first-order statistics...

A New Nonparametric Test for Two Sample Multivariate Location Problem with Application to Astronomy

Soumita Modak, Uttam Bandyopadhyay
Pages: 136 - 146
This paper provides a nonparametric test for the identity of two multivariate continuous distribution functions when they differ in locations. The test uses Wilcoxon rank-sum statistics on distances between observations for each of the components and is unaffected by outliers. It is numerically compared...

A New Generalized Two-Sided Class of the Distributions Via New Transmuted Two-Sided Bounded Distribution

O. Kharazmi, M. Zargar
Pages: 87 - 102
In the present paper, we first consider a generalization of the standard two-sided power distribution so-called the transmuted two-sided distribution, and then extend proposed idea to generalized two-sided class of distributions, introduced by Korkmaz and Genç [1]. Some statistical and reliability properties...

A Multivariate Skew-Normal Mean-Variance Mixture Distribution and Its Application to Environmental Data with Outlying Observations

M. Tamandi, N. Balakrishnan, A. Jamalizadeh, M. Amiri
Pages: 244 - 258
The presence of outliers, skewness, kurtosis, and dependency are well-known challenges while fitting distributions to many data sets. Developing multivariate distributions that can properly accomodate all these aspects has been the aim of several researchers. In this regard, we introduce here a new multivariate...

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...

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...

On the Influence Function for the Theil-Like Class of Inequality Measures

Tchilabalo Abozou Kpanzou, Diam Ba, Pape Djiby Mergane, Gane Samb LO
Pages: 270 - 277
On one hand, a large class of inequality measures, which includes the generalized entropy, the Atkinson, the Gini, etc., for example, has been introduced in P.D. Mergane, G.S. Lo, Appl. Math. 4 (2013), 986–1000. On the other hand, the influence function (IF) of statistics is an important tool in the...

On a Generalized Burr Life-Testing Model: Characterization, Reliability, Simulation, and Akaike Information Criterion

M. Ahsanullah, M. Shakil, B. M. Golam Kibria, M. Elgarhy
Pages: 259 - 269
For a continuous random variable X, M. Shakil, B.M.G. Kibria, J. Stat. Theory Appl. 9 (2010), 255–282, introduced a generalized Burr increasing, decreasing, and upside-down bathtub failure rate life-testing model. In this paper, we provide some characterizations of this life-testing model by truncated...

Characterization of Exponential Distribution Through Normalized Spacing of Generalized Order Statistics

M. J. S. Khan, S. Iqrar, M. Faizan
Pages: 303 - 308
In this paper, exponential distribution is characterized by normalized spacing of generalized order statistics (gos) using Meijer's G-function. While the necessary part of the theorem was given by U. Kamps, E. Cramer, Statistics. 35 (2001), 269–280, we have given an easy proof of sufficient part in this...

E-Bayesian Estimation for the Exponential Model Based on Record Statistics

Hassan M. Okasha
Pages: 236 - 243
This paper is concerned with using the E-Bayesian method for computing estimates for the parameter and reliability function of the Exponential distribution based on a set of upper record statistics values. The estimates are derived based on a conjugate prior for the scale parameter and squared error...

Discriminating Between Exponential and Lindley Distributions

V. S. Vaidyanathan, A Sharon Varghese
Pages: 295 - 302
In literature, Lindley distribution is considered as an alternate to the exponential distribution. In the present work, a methodology is developed to discriminate between exponential and Lindley distributions based on the ratio of the maximum likelihoods. Asymptotic distribution of the test statistic...

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...