Journal of Statistical Theory and Applications

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266 articles

Preservation of Classes of Discrete Distributions Under Reliability Operations

I. Elbatal, M. Ahsanullah
Pages: 1 - 10
In this paper we consider some widely utilized classes of discrete distributions and aim to provide a systematic overview about their preservation under convolution. This paper will serve as a detailed reference for the study and applications of the preservation of the discrete NBU(2), NBUCA classes...

On Marshall-Olkin Extended Weibull Distribution

Hanan Haj Ahmad, Omar M. Bdair, M. Ahsanullah
Pages: 1 - 17
In this paper, we introduce a new form of distributions called ”Marshall-Olkin Extended Weibull distribution” MOEW. We study some of its structural properties and the shape of its hazard rate function. We provide some methods of point estimation for the unknown parameters and discuss its asymptotic properties....

Concomitants of Dual Generalized Order Statistics from Morgenstern Type Bivariate Generalized Exponential Distribution

Saeid Tahmasebi, Ali Akbar Jafari, Mahmoud Afshari
Pages: 1 - 12
[9] introduced the concept of dual generalized order statistics (dgos) that enables a common approach to descending ordered random variables like reversed order statistics and lower record values. In this paper, we have obtained probability density function (pdf) of r-th, and the joint pdf of r-th and...

The gamma extended Weibull family of distributions

Abraao D.C. Nascimento, Marcelo Bourguignon, Luz M. Zea, Manoel Santos-Neto, Rodrigo B. Silva, Gauss M. Cordeiro
Pages: 1 - 16
We introduce a new family of distributions called the gamma extended Weibull family. The proposed family includes several well-known models as special cases and defines at least seventeen new special models. Structural properties of this family are studied. Additionally, the maximum likelihood method...

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...

Bayesian Estimation of the Scale Parameter of the Marshall-Olkin Exponential Distribution under Progressively Type-II Censored Samples

Mukhtar M. Salah
Pages: 1 - 14
This paper studies the Bayes estimator, the maximum likelihood estimator and the approximate likelihood estimator of the scale parameter for the Marshall-Olkin exponential distribution under the progressive type-II censored sample. All the estimators, Bayes estimator, maximum likelihood estimator and...

The Exponentiated Kumaraswamy InverseWeibull Distribution with Application in Survival Analysis

J.A. Rodrigues, A.P.C.M. Silva, G.G. Hamedani
Pages: 8 - 24
In this paper, a new distribution called the exponentiated Kumaraswamy inverse Weibull is proposed. This dis- tribution includes as special cases the inverse exponential, inverseWeibull, inverse Rayleigh and exponentiated inverse Weibull distributions. We study the main properties of this distribution,...

Characterizations of Certain Recently Introduced Distributions

G.G. Hamedani
Pages: 11 - 20
Various characterizations of the Beta Weibull Geometric distribution of Bidram et al. (2011), the New Generalized Exponential distribution of Bidram et al. (2012), and the Gamma Exponentiated Weibull distribution of Pinho et al. (2012) are presented. These characterizations are based on: (i) a simple...

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...

Assessment of Cpm in the presence of measurement errors

Amit K. Baral, M.Z. Anis
Pages: 13 - 27
With the advent of Taguchi’s loss function, the concept of target and sticking to the target to achieve better process performance has become widely accepted. In practice, while estimating process performance, the gauge measurement error is not taken into consideration. In the real world scenario this...

Results on Cumulative Measure of Inaccuracy in Record Values

Saeid Tahmasebi, Ahmad Nezakati, Safeih Daneshi
Pages: 15 - 28
In this paper, we propose cumulative measure of inaccuracy in lower record values and study characterization results in case of dynamic cumulative inaccuracy. We also discuss some properties of the proposed measures. Finally, we study a problem of estimating the cumulative measure of inaccuracy by means...

A Note on a Characterization of Gompertz-Verhulst Distribution

M. Ahsanullah, M. Shakil, B.M. Golam Kibria
Pages: 17 - 26
Characterization of a probability distribution plays an important role in probability and statistics. This paper considers a new characterization of Gompertz-Verhulst distribution. It is hoped that the findings of the paper will be useful for researchers in different fields of applied sciences.

Characterizations of the Generalized Beta-generated family of distributions

G. G. Hamedani, V. Mameli
Pages: 18 - 25
Several characterizations of Generalized Beta-generated family of distributions, introduced by Alexander et al. (2012), are presented, giving special emphasis to the Kumaraswamy skew-normal distribution and the Beta skew-normal distribution, special cases of this family. These characterizations are based...

Parameter Estimation in Gamma Mixture Model using Normal-based Approximation

R. Vani Lakshmi, V.S. Vaidyanathan
Pages: 25 - 35
Gamma mixture models have wide applications in hydrology, finance and reliability. Parameter estimation in this class of models is a challenging task owing to the complexity associated with the model structure. In this paper, a novel approach is proposed to estimate the parameters of Gamma mixture models...

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...

An Efficient Estimation Procedure in Two-Occasion Successive Sampling

G. N. Singh, A. K. Singh
Pages: 26 - 37
In this paper an efficient estimation procedure to estimate the current population mean in two-occasion successive sampling has been developed. An exponential regression type estimator of current population mean is proposed and corresponding optimum replacement strategy has been suggested. The superiority...

Stochastic Comparisons of Residual Entropy of Order Statistics and Some Characterization Results

Ramesh C. Gupta, H.C. Taneja, Richa Thapliyal
Pages: 27 - 37
In this paper, we have presented some results for the residual and past entropies of order statistics. Results on the stochastic comparisons based on residual entropy of order statistics are presented. Characterization results for these dynamic entropies based on the sufficient condition for the uniqueness...

A generalization of Tukey’s g-h family of distributions

J.A. Jiménez, V. Arunachalam, G.M. Serna
Pages: 28 - 44
A new class of distribution function based on the symmetric densities is introduced, these transformations also produce nonnormal distributions and its pdf and cd f can be expressed in parametric form. This class of distributions depend on the two parameters, namely g and h which controls the skewness...

LINEX K-Means: Clustering by an Asymmetric Dissimilarity Measure

Narges Ahmadzadehgoli, Adel Mohammadpour, Mohammad Hassan Behzadi
Pages: 29 - 38
Clustering is a well-known approach in data mining, which is used to separate data without being labeled. Some clustering methods are more popular such as the k-means. In all clustering techniques, the cluster centers must be found that help to determine which object is belonged to which cluster by measuring...

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...

EM Algorithm and Positive Quadrant Dependence in the context of Multi-State Stress-Strength Model

Sanjeev Sabnis, Mayank Jain, Kartik Verma
Pages: 36 - 46
This research article is related to a multi-state stress-strength model proposed by Eryilmaz and İşçioğlu (2011). It deals with (i) demonstration of the use of EM algorithm for the estimation of parameters of distributions of random variables representing strength and two stress levels. The numerical...

On Characterization of Gompertz Distribution by Properties of Generalized Record Values

S. Minimol, P. Yageen Thomas
Pages: 38 - 45
In this chapter, we derive some recurrence relations satisfied by single and product moments of generalized record values arising from Gompertz and inverted Gompertz distributions. Further, we have obtained characterization of Gompertz and inverted Gompertz distributions based on certain properties of...

On Some New Results of Poverty Orderings and Their Applications

Mervat Mahdy
Pages: 38 - 52
The paper proposes to derive some new poverty indices which depend on aging classes. We also give some properties of it and show the connection between economic measure and new poverty measures these based on the concept of reversed residual incomes. In addition, the characterization of Pareto distribution...

A New Lifetime Model: The Gamma Extended Fréchet Distribution

Ronaldo V. da Silva, Thiago A.N. de Andrade, Diego B.M. Maciel, Renilma P. S. Campos, Gauss M. Cordeiro
Pages: 39 - 54
For the first time, a four-parameter lifetime model, called the gamma extended Fr´echet distribution, is defined and studied. We obtain some of its mathematical properties. Explicit expressions for the ordinary and incomplete moments, quantile function, mean deviations, R´enyi entropy and reliability...

A New Method for Generating Discrete Analogues of Continuous Distributions

M. Ganji, F. Gharari
Pages: 39 - 58
In this paper we use discrete fractional calculus for showing the existence of delta and nabla discrete distributions and then apply time scales for definition of delta and nabla discrete gamma distributions. The main result of this paper is unification of the continuous and discrete gamma distributions,...

Generalized Estimator of Finite population Variance

A.K.P.C. Swain
Pages: 45 - 51
In this paper a generalized class of finite population variance is suggested and its large sample bias and mean square error are derived. Further some special cases of this class are considered along with a numerical example to compute and compare their biases and mean square errors.

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...

Estimation of a Matrix of Heterogeneity Parameters in Multivariate Meta-Analysis of Random-Effects Models

Abera Wouhib
Pages: 46 - 64
Multivariate meta-analysis has potential over its univariate counterpart. The most common challenge in univariate or multivariate meta-analysis is estimating heterogeneity parameters in non-negative domains under the random-effects model assumption. In this context, two new multivariate estimation methods...

Pathway Extension of Weibull-Gamma Model

T. Princy
Pages: 47 - 60
In this paper we develop a new family of Weibull-gamma model which is obtained by compounding a q-Weibull density with a two parameter gamma density. This class can be considered as a natural extension of the Weibull gamma model which accommodates various other useful statistical models. Properties...

Edgeworth Expansion of the Parametric Bootstrap t-statistic for Linear Regression Processes with Strongly Dependent Errors

Mosisa Aga
Pages: 52 - 59
The purpose of this paper is to provide a valid Edgeworth expansion for the parametric bootstrap t-statistic of a linear regression process whose error terms are stationary, Gaussian, and strongly dependent time series. Under some sets of conditions on the spectral density function and the parametric...

Bayesian analysis of hierarchical heteroscedastic linear models using Dirichlet-Laplace priors

S. K. Ghoreishi
Pages: 53 - 64
From practical point of view, in a two-level hierarchical model, the variance of second-level usually has a tendency to change through sub-populations. The existence of this kind of local (or intrinsic ) heteroscedasticity is a major concern in the application of statistical modeling. The main purpose...

A Symmetric Component Alpha Normal Slash Distribution: Properties and Inferences

Wenhao Gui, Pei-Hua Chen, Haiyan Wu
Pages: 55 - 66
In this paper, we introduce a new class of symmetric bimodal distribution. We define the distribution by means of a stochastic representation as the mixture of a symmetric component alpha normal random variable with respect to the power of a uniform random variable. The proposed distribution is more...

The Kumaraswamy Marshall-Olkin Log-Logistic Distribution with Application

Selen Cakmakyapan, Gamze Ozel, Yehia Mousa Hussein El Gebaly, G. G. Hamedani
Pages: 59 - 76
In this paper, we define and study a new lifetime model called the Kumaraswamy Marshall-Olkin log-logistic distribution. The new model has the advantage of being capable of modeling various shapes of aging and failure criteria. The new model contains some well-known distributions as special cases such...

The beta exponentiated Lindley distribution

J.A. Rodrigues, A.P.C.M. Silva, G.G. Hamedani
Pages: 60 - 75
In this work, we study the beta exponentiated Lindley distribution which includes as special cases several models such as the Lindley, exponentiated Lindley and beta Lindley distributions. Some structural properties of the proposed distribution are studied including expressions for the moments. The estimation...

The Gumbel-Lomax Distribution: Properties and Applications

M.H. Tahir, M. Adnan Hussain, Gauss M. Cordeiro, G.G. Hamedani, M. Mansoor, M. Zubair
Pages: 61 - 79
We introduce a new four-parameter model called the Gumbel-Lomax distribution arising from the Gumbel- X generator recently proposed by Al-Aqtash (2013). Its density function can be right-skewed and reversed-J shaped, and can have decreasing and upside-down bathtub shaped hazard rate....

McDonald log-logistic distribution with an application to breast cancer data

M.H. Tahir, Muhammad Mansoor, Muhammad Zubair, G.G. Hamedani
Pages: 65 - 82
We introduce a five-parameter continuous model, called the McDonald log-logistic distribution, to extend the two-parameter log-logistic distribution. Some structural properties of this new distribution such as reliability measures and entropies are obtained. The model parameters are estimated by the...

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...

Transmuted Generalized Gompertz distribution with application

Muhammad Shuaib Khan, Robert King, Irene Lena Hudson
Pages: 65 - 80
This paper introduces the four parameter transmuted generalized Gompertz distribution which includes the transmuted Gompertz, transmuted generalized exponential, transmuted exponential, Gompertz, generalized exponential and exponential distributions as special cases and studies its statistical properties....

Prediction Intervals for k-records in Terms of Current Records

M. Chahkandi, J. Ahmadi
Pages: 67 - 82
In this paper, we discuss the prediction of k-records from the future sequence based on observed current records of either kind upper or lower, record coverage and k-records from the same distribution. It is shown that the coverage probability of all proposed prediction intervals are distribution-free....

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...

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,...

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...

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...

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...

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...

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.

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,...

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...