Journal of Statistical Theory and Applications

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293 articles
Research Article

Stochastic Properties of the Weighted Hazard Rate Order

S. Izadkhah, M. Amini, G.R. Mohtashami Borzadaran
Pages: 76 - 88
The hazard rate order between two weighted distributions with a given weight function is considered as a new stochastic order called weighted hazard rate order. The influences of biased sampling methods on properties of the hazard rate order are usefully pointed out with this weighted order. We first...
Research Article

Odd Generalized Exponential Flexible Weibull Extension Distribution

Abdelfattah Mustafa, Beih S. El-Desouky, Shamsan AL-Garash
Pages: 77 - 90
In this article we introduce a new four - parameters model called the odd generalized exponential flexible Weibull extension (OGE-FWE) distribution which exhibits bathtub-shaped hazard rate. Some of it’s statistical properties are obtained including ordinary and incomplete moments, quantile and mode,...
Research Article

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...
Research Article

Multi-stage Optional Unrelated Question RRT Model

Anu Chhabra, B.K. Dass, Samridhi Mehta
Pages: 80 - 95
Sihm et al. (2014) introduced modified optional unrelated question RRT model in both binary and quantitative response situations wherein the prevalence of the sensitive variable and the sensitivity level of the underlying sensitive question could be estimated simultaneously without using a split sample...
Research Article

A study of methods for estimating in the exponentiated Gumbel distribution

K. Fathi, S.F. Bagheri, M. Alizadeh, M. Alizadeh
Pages: 81 - 95
The exponentiated Gumbel model has been shown to be useful in climate modeling including global warming problem, flood frequency analysis, offshore modeling, rainfall modeling and wind speed modeling. Here, we consider estimation of the PDF and the CDF of the exponentiated Gumbel distribution. The following...
Research Article

On Some Predictive Ratio Type Estimators in Two Stage Sampling

A.K.P.C. Swain, Sitanshu Shekhar Mishra, B.K. Pradhan
Pages: 83 - 91
Some predictive ratio type estimators in two stage sampling are derived following the model free predictive criterion proposed by Basu (1971) and these estimators are compared with the classical multistage ratio estimator and also with Smith’s (1969) multistage ratio estimator. A numerical illustration...
Short Communication

A characterization of the normal distribution

Hans Volkmer
Pages: 83 - 85
It is shown that the normal distribution with mean zero is characterized by the property that the product of its characteristic function and moment generating function is equal to 1.
Research Article

Some new results for the Kumaraswamy modified Weibull distribution

Gauss M. Cordeiro, Antonio C.R. Braga Junior, Clarice G.B. Demétrio, Edwin M.M. Ortega, Rodrigo R. Pescim
Pages: 86 - 104
We study some mathematical properties of the Kumaraswamy modified Weibull distribution pioneered by Cordeiro et al. [4] not discussed by these authors. This model is quite flexible for analyzing positive data since it contains as special models some widely-known distributions, such as the KumaraswamyWeibull,...
Research Article

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...
Research Article

On the Properties of Estimates of Monotonic Mean Vectors for Multivariate Normal Distributions

Abouzar Bazyari
Pages: 89 - 106
.Problems concerning estimation of parameters and determination the statistic, when it is known a priori that some of these parameters are subject to certain order restrictions, are of considerable interest. In the present paper, we consider the estimators of the monotonic mean vectors for two dimensional...
Research Article

Fuzzy C-Means Clustering Using Asymmetric Loss Function

Israa Abdzaid Atiyah, Adel Mohammadpour, Narges Ahmadzadehgol, S. Mahmoud Taheri
Pages: 91 - 101
In this work, a fuzzy clustering algorithm is proposed based on the asymmetric loss function instead of the usual symmetric dissimilarities. Linear Exponential (LINEX) loss function is a commonly used asymmetric loss function, which is considered in this paper. We prove that the negative likelihood of...
Research Article

Combined Intra- and Inter- Block Analysis of Balanced Ternary Designs

Sobita Sapam, B. K. Sinha, N.K. Mandal
Pages: 91 - 100
In the present paper an attempt has been made to study the inter–and intra-block estimation of treatment effects contrasts with random block effects in the context of balanced ternary designs. The analysis is illustrated through examples.
Research Article

Multiplicative-Binomial Distribution: Some Results on Characterization, Inference and Random Data Generation

Elsayed A.H. Elamir
Pages: 92 - 105
Multiplicative-binomial distribution is one of the distributions that allows for over-dispersion and under-dispersion relative to the standard binomial distribution. It will be shown that the multiplicative-binomial distribution can be a very useful model for these situations. Moreover, the confidence...
Research Article

On the Parametric Maximum Likelihood Estimator for Independent but Non-identically Distributed Observations with Application to Truncated Data

Fanny Leroy, Jean-Yves Dauxois, Pascale Tubert-Bitter
Pages: 96 - 107
We investigate the parametric maximum likelihood estimator for truncated data when the truncation value is different according to the observed individual or item. We extend Lehmann’s proof (1983) of the asymptotic properties of the parametric maximum likelihood estimator in the case of independent nonidentically...
Research Article

Optimal Structure (k) Designs for Comparing Test Treatments with a Control

M. A. Chowdhury, S. Mandal, D. K. Ghosh, S. C. Bagui
Pages: 96 - 107
Mukerjee (1979) introduced structure (k) property of a factorial design. In this article, we introduce structure (k1), structure (k2) and structure (k1k2) properties of a factorial design. We establish properties of each of...
Research Article

On Some Aspects of a New Class of Two-Piece Asymmetric Normal Distribution

C. Satheesh Kumar, M.R. Anusree
Pages: 101 - 121
Through this chapter, we introduce a new class of two-piece asymmetric normal distribution suitable for asymmetric and plurimodal situations. We study some important aspects of this distribution by deriving explicit expressions for its distribution function, characteristic function, reliability measures...
Research Article

A New Flexible Discrete Distribution with Applications to Count Data

Anwar Hassan, Gulzar Ahmad Shalbaf, Sheikh Bilal, Adil Rashid
Pages: 102 - 108
In this paper we have explored a new discrete probability mass function that has been generated through compounding mechanism. This newly proposed probability mass function is essentially a mixture of Poisson and Ailamujia distribution. Furthermore the parameter estimation has also been discussed by...
Research Article

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...
Research Article

Beta Burr XII OR Five Parameter Beta Lomax Distribution: Remarks and Characterizations

Z. Javanshiri, M. Maadooliat
Pages: 105 - 110
The distributions taken up in two recently published papers are compared and certain characterizations of them are presented. These characterizations are based on: (i) a simple relationship between two truncated moments; (ii) truncated moments of certain functions of the nth order statistic; (iii) truncated...
Research Article

New classes at Specific Age: Properties and Testing hypotheses

M.A.W. Mahmoud, M.E. Moshref, A.M. Gadallah, A.I. Shawky
Pages: 106 - 119
In this article we introduce new classes of life distributions namely new better (worse) than used in expectation at specific age t0 NBUE-t0 (NWUE-t0) and harmonic new better (worse) than used in expectation at specific age t0 HNBUE-t0 (HNWUE-t0). The closure properties under various reliability operations...
Research Article

Bayesian Estimation Based on Progressively Type-II Censored Samples from Compound Rayleigh Distribution

Rashad Mohamed EL-Sagheer, Mohamed Ahsanullah
Pages: 107 - 122
This paper considers inference under progressive type-II censoring scheme with a compound Rayleigh failure time distribution. The maximum likelihood (ML) and the Bayes estimators for the two unknown parameters of the compound Rayleigh distribution (CRD) distribution are derived. A Bayesian approach using...
Research Article

Likelihood Inference in A Multivariate Spatial GLMM with Skew Gaussian Random Effects Using the Slice-SAB Algorithm

Firoozeh Rivaz, Majid Jafari Khaledi
Pages: 108 - 116
This paper introduces a multivariate skew Gaussian process and uses it to extend the family of multivariate spatial generalized linear mixed models to include skew Gaussian random effects. In this setting, the param- eter estimation encounters problems because the likelihood function involves high dimensional...
Research Article

Characterizing Distributions by Linearity of Regression of Generalized Order Statistics

Abbas Rasouli, S. Samadi, Mohammad Ahsanullah
Pages: 108 - 114
Let X1,..., Xn be a random sample from an absolutely continuous (with respect to Lebesgue measure) distribution with the corresponding generalized order statistics X(1, n, m~, k),..., X(n, n, m~,...
Research Article

Sample Design and Estimation of Parameters of Half Logistic Distribution Using Generalized Ranked-Set Sampling

A. Adatia, A.K.MD. Ehsanes Saleh
Pages: 109 - 117
The ranked-set sampling technique has been generalized so that a more efficient estimator may be obtained. This technique allows more than one unit from each set to be quantified. Consequently, the number of units to be sampled may be reduced significantly and as a result, the corresponding cost would...
Research Article

Testing Exponentiality Against UBAC Using Kernel Methods

M.M. Mohie El-Din, S.E. Abu-Youssef, M.KH. Hassan
Pages: 111 - 121
In this paper, the problem of testing exponentiality against used better than aged in convex ordering classes of life distributions is investigated. For this property a nonparametric test is presented based on kernel method. The test is presented for complete and right censored data. Furthermore, Pitman's...
Research Article

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....
Research Article

Moments of Record Values and Characterizations of Marshall-Olkin Extended Distribution

G.G. Hamedani, Miroslav M. Ristić
Pages: 115 - 124
Moments of the mth upper record value XU(m), m≥1, and the joint moments of the mth and nth upper record values XU(m) and XU(n), n>m≥1,...
Research Article

Bayesian Analysis of a 3-Component Mixture of Rayleigh Distributions under Type-I Right Censoring Scheme

Muhammad Tahir, Muhammad Aslam, Zawar Hussain
Pages: 117 - 136
Since the last few decades, constructing flexible parametric classes of probability distributions has been the most popular approach in the Bayesian analysis. As compared to simple probability models, a mixture model of some suitable lifetime distributions may be more capable of capturing the heterogeneity...
Research Article

Robust Mixture Regression Based on the Mixture of Slash Distributions

Hadi Saboori, Ghobad Barmalzan, Mahdi Doostparast
Pages: 118 - 132
The traditional estimation of Mixture regression models is based on the normal assumption of component errors and thus is sensitive to outliers and heavy-tailed errors. In this paper, we propose a robust Mixture regression models in which a mixture of slash distributions is assumed for the errors. Using...
Research Article

On Discrete Residual and Past Measures of Inaccuracy

Vikas Kumar, Richa Thapliyal, H.C. Taneja
Pages: 120 - 128
The present communication considers a discrete dynamic measure of inaccuracy between two residual and past lifetime distributions. Under the assumption that the true distribution F and reference distribution G satisfy the proportional hazard model (PHM) and proportional reversed hazard model (PRHM),...
Research Article

Estimating the parameters of Lomax distribution from imprecise information

Abbas Pak, Mohammad Reza Mahmoudi
Pages: 122 - 135
Traditional statistical approaches for estimating the parameters of Lomax distribution have dealt with precise information. However, in real world situations, some information about an underlying system might be imprecise and are represented in the form of fuzzy information. In this paper, we consider...
Research Article

The Kumaraswamy-Half-Cauchy distribution: properties and applications

Indranil Ghosh
Pages: 122 - 134
In this article, based on the half-Cauchy distribution, we propose a new distribution called Kumaraswamy- Half-Cauchy distribution. Various explicit expressions for it’s moments, generating and quantile functions, mean deviations, reliability parameter, density function of the order statistics and their...
Research Article

Recurrence Relations for Single and Product Moments of Dual Generalized Order Statistics from a General Class of Distributions

Jagdish Saran, Narinder Pushkarna, Rashmi Tiwari
Pages: 123 - 130
In this paper we derive some general recurrence relations between single and product moments of dual gener- alized order statistics from a general class of distributions, thus generalizing and unifying the earlier results in this direction due to several authors.
Research Article

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...
Research Article

The Additive Weibull-Geometric Distribution: Theory and Applications

I. Elbatal, M.M. Mansour, Mohammad Ahsanullah
Pages: 125 - 141
In this paper, we introduce a new class of lifetime distributions which is called the additive Weibull geometric (AWG) distribution. This distribution obtained by compounding the additive Weibull and geometric distributions. The new distribution has a number of well-known lifetime special sub-models...
Research Article

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...
Research Article

The Kumaraswamy Pareto distribution

Marcelo Bourguignon, Rodrigo B. Silva, Luz M. Zea, Gauss M. Cordeiro
Pages: 129 - 144
The modeling and analysis of lifetimes is an important aspect of statistical work in a wide variety of scientific and technological fields. For the first time, the called Kumaraswamy Pareto distribution, is introduced and studied. The new distribution can have a decreasing and upside-down bathtub failure...
Research Article

On Some Nonparametric Tests For Partially Observed Correlated Data: Proposing New Tests

Hani M. Samawi, Lili Yu, Robert Vogel
Pages: 131 - 155
Correlated or matched data is frequently collected under many study designs in applied sciences such as the social, behavioral, economic, biological, medical, epidemiologic, health, public health, and drug developmental sciences in order to have more efficient design and to control for potential confounding...
Research Article

Modeling Vehicle Insurance Loss Data Using a New Member of T-X Family of Distributions

Zubair Ahmad, Eisa Mahmoudi, Sanku Dey, Saima K. Khosa
Pages: 133 - 147
In actuarial literature, we come across a diverse range of probability distributions for fitting insurance loss data. Popular distributions are lognormal, log-t, various versions of Pareto, log-logistic, Weibull, gamma and its variants and a generalized beta of the second kind, among others. In this...
Research Article

On Moment Generating Function of Generalized Order Statistics From Extended Type II Generalized Logistic Distribution

Devendra Kumar
Pages: 135 - 150
In this paper, explicit expressions and some recurrence relations are derived for marginal and joint moment generating functions of generalized order statistics from extended type II loglogistic distribution. Further the results are deduced for moments of k -- th record values and ordinary order statistics.
Research Article

Estimating Quantiles of Two Exponential Populations with a Common Location Parameter Using Censored Samples

Adarsha Kumar Jena, Manas Ranjan Tripathy
Pages: 136 - 145
Estimation of quantiles of two exponential populations is considered assuming equality of location parameters using censored samples from a decision theoretic point of view. Sufficient conditions for inadmissibility of estimators in certain classes have been derived. Consequently some complete class...
Research Article

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...
Research Article

Recurrence Relations for Moments of Generalized Order Statistics for Inverse Weibull Distribution and Some Characterizations

Saman Hanif Shahbaz, Mohammad Ahsanullah, Muhammad Qaiser Shahabaz
Pages: 137 - 149
We present recurrence relations for single, inverse, product and ratio moments of Generalized Order Statistics when sample is available from an Inverse Weibull Distribution. These relations enable computation of higher order moments using corresponding lower order moments. Some Characterizations of the...
Research Article

Some Modified Mean Estimators in Ranked Set Sampling Using a Covariate

Ehsan Zamanzade, Mohammad Mohammadi
Pages: 142 - 152
In this paper we modify nonparametric regression-based mean estimators in ranked set sampling using a covariate. We will show that our modified mean estimators perform well in comparison with their leading competitors.
Research Article

Laws of the iterated logarithm for nonparametric sequential density estimators

Karima Lagha, Smail Adjabi
Pages: 145 - 151
In this note, we establish a law of iterated logarithm for a triangular array of a random number of independent random variables and apply it to obtain laws of iterated logarithm for the sequential nonparametric density estimators. We consider the case of Rosenblatt-Parzen kernel estimators and orthogonal...
Research Article

Bayesian Inference Based on Multiply Type-II Censored Sample from a General Class of Distributions

A.R. Shafay, M.M. Mohie El-Din, Y. Abdel-Aty
Pages: 146 - 157
In this paper, we consider a general form for the underlying distribution and a general conjugate prior, and develop a general procedure for Bayesian estimation based on an observed multiply Type-II censored sample. The problem of predicting the order statistics from a future sample are also discussed...
Research Article

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...
Research Article

Empirical Estimation for Sparse Double-Heteroscedastic Hierarchical Normal Models

Vida Shantia, S. K. Ghoreishi
Pages: 148 - 161
The available heteroscedastic hierarchical models perform well for a wide range of real-world data, but for the data sets which exhibit heteroscedasticity mainly due to the lack of constant means rather than unequal variances, the existing models tend to overestimate the variance of the second level...
Research Article

Cure Rate Models Considering The Burr XII Distribution in Presence of Covariate

Emílio A. Coelho-Barros, Jorge Alberto Achcar, Josmar Mazucheli
Pages: 150 - 164
This paper presents estimates for the parameters included in long-term mixture and non-mixture lifetime models, applied to analyze survival data when some individuals may never experience the event of interest. We consider the case where the lifetime data have a three-parameter Burr XII distribution,...
Research Article

Bayesian Prediction in Clipped GLG Random Field Using Slice Sampling

Majid Jafari Khaledi, Hamidreza Zareifard, Firoozeh Rivaz
Pages: 151 - 161
By assuming that an underlying Gaussian-Log Gaussian (GLG) random field clipped to yield binary spatial data, we propose a new model which provides flexibility in capturing the effects of heavy tail in latent variables. For our analysis, we adopt a Bayesian framework and develop a Markov chain Monte...