Journal of Statistical Theory and Applications

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292 articles
Research Article

The Zografos-Balakrishnan Log-Logistic Distribution: Properties and Applications

Manoel Wallace A. Ramos, Gauss M. Cordeiro, Pedro Rafael D. Marinho, Cicero Rafael B. Dias, G.G. Hamedani
Pages: 225 - 244
The log-logistic distribution (also known as the Fisk distribution in economics) is widely used in survival analysis when the failure rate function presents a unimodal shape. In this paper, we introduce the Zografos- Balakrishnan log-logistic distribution, which contains the log-logistic distribution...
Research Article

A note on Sum, Difference, Product and Ratio of Kumaraswamy Random Variables

Avishek Mallick, Indranil Ghosh, G. G. Hamedani
Pages: 230 - 241
Explicit expressions for the densities of S = X1 + X2 , D = X1 − X2 , P = X1X2 and R = X1/X2 are derived when X1 and X2 are independent or sub-independent Kumaraswamy random variables. The expressions appear to involve the incomplete gamma functions. Some possible real life scenarios are mentioned in...
Research Article

Analysis of Covariance of Reinforced Balanced Incomplete Block Designs With a Single Explanatory Variable

D.K. Ghosh, M.G. Bhatt, S.C. Bagui
Pages: 235 - 246
Reinforced balanced incomplete block designs (BIBDs) are very useful in statistical planning of experiments as they can be constructed for any number of treatments for given numbers of replications. Das (1958) was first to introduce the statistical analysis of variance (ANOVA) of these designs, and in...
Research Article

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...
Research Article

A generalized asymmetry model for square contingency tables with ordered categories

Kiyotaka Iki, Takahiro Suto, Sadao Tomizawa
Pages: 237 - 247
For square contingency tables with ordered categories, the present paper proposes an asymmetry model with m-additional parameters, which indicates (1) the generalized marginal homogeneity and (2) the structure of quasi-symmetry for cumulative probabilities. The proposed model includes a modified...
Research Article

Comparing Two Means Using Partially Paired and Unpaired Data

Nizam Uddin, Mohamad S. Hasan
Pages: 238 - 247
A new test statistic is proposed to test the equality of two normal means when the data is partially paired and partially unpaired. The test statistic is based on a linear combination of the differences of both paired and unpaired sample means. Using t-distribution as the approximate null distribution,...
Research Article

E-Bayesian Estimation for Rayleigh Model Using Progressive Type-II Censoring Data

Rashad Mohamed EL-Sagheer
Pages: 239 - 247
This article deals with using E-Bayesian method under progressively type-II censored sample from the Rayleigh distribution (RD) for computing the estimates of the parameter. The Bayesian and E-Bayesian estimators are obtained under squared error and LINEX loss functions. A comparison between E-Bayesian...
Research Article

Concomitants of Dual Generalized Order Statistics from Bivariate Burr III Distribution

Haseeb Athar, Nayabuddin, Zuber Akhter
Pages: 240 - 256
In this paper probability density function of single concomitant and joint probability density function of two concomitants of dual generalized order statistics from bivariate Burr III distribution are obtained and expressions for single and product moments are derived. Further, results are deduced for...
Research Article

Estimating the Modified Weibull Parameters in Presence of Constant-Stress Partially Accelerated Life Testing

Mohamed A. W. Mahmoud, Rashad M. EL-Sagheer, Amr M. Abou-Senna
Pages: 242 - 260
Accelerated life testing is very important in life testing experiments because it saves time and cost. In this paper, assuming that the lifetime of items under use condition follows the modified Weilbull distribution, partially accelerated life tests based on progressive Type-II censored samples are...
Research Article

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...
Research Article

Parameters Estimation in a General Failure Rate Semi-Markov Reliability Model

M. Fathizadeh, K. Khorshidian
Pages: 245 - 252
A semi-Markov process with four states, has been applied for modeling two dissimilar unit cold standby systems. At the moment that operating unit fails, the standby unit is switched to operate by using a switching device that is available with unknown probability alpha1. It is also assumed that the failure...
Research Article

On Record Values and Reliability Properties of Marshall–Olkin Extended Exponential Distribution

K.K. Jose, E. Krishna, Miroslav M. Ristic
Pages: 247 - 262
The Marshall–Olkin Extended Exponential distribution is introduced and reliability properties are studied. The p.d.f.’s of nth record value, joint p.d.f.’s, of mth and nth record values are derived to obtain the expression for mean, variance and covariance of reord values. The entropy of jth record value...
Research Article

Tests for Comparing Several Two-Parameter Exponential Distributions Based on Uncensored/Censored Samples

K. Krishnamoorthy, Thu Nguyen, Yongli Sang
Pages: 248 - 260
The problems of comparing several exponential distributions based on type II censored samples are considered. Likelihood ratio tests (LRTs) for comparing several location parameters, comparing several scale parameters and for homogeneity of distributions are derived. The LRTs for all three problems are...
Research Article

Bayesian Estimation of the Kumaraswamy Inverse Weibull Distribution

Felipe R.S. de Gusmão, Vera L.D. Tomazella, Ricardo S. Ehlers
Pages: 248 - 260
The Kumaraswamy InverseWeibull distribution has the ability to model failure rates that have unimodal shapes and are quite common in reliability and biological studies. The three-parameter Kumaraswamy InverseWeibull distribution with decreasing and unimodal failure rate is introduced. We provide a comprehensive...
Research Article

Ordered extreme ranked set sampling and its application in parametric estimation

Manoj Chacko
Pages: 248 - 258
Ranked set sampling (RSS) is applicable whenever ranking of a set of sampling units can be done easily by a judgment method or based on the measurement of an auxiliary variable which can be measured easily. In this work, a modification of RSS called ordered extreme ranked set sampling is considered for...
Research Article

On Estimating Residual Heterogeneity in Random-Effects Meta-Regression: A Comparative Study

Thammarat Panityakul, Chinnaphong Bumrungsup, Guido Knapp
Pages: 253 - 265
We consider six different estimators of residual heterogeneity in random-effects meta-regression, five estimators already known and implemented in the R package metaphor and one estimator not yet considered in random-effects meta-regression. In a numerical study, we investigate the properties of these...
Research Article

Three Characterizations of Exponential Distribution Involving Median of Sample of Size Three

Marko Obradovic
Pages: 257 - 264
In this paper three new characterizing theorems of exponential distribution are presented. They are based on equidistribution of some functions of order statistics. All of them include the median of sample of size three
Research Article

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...
Research Article

Recurrence Relations for Marginal and Joint Moment Generating Functions of Generalized Order Statistics from a New Class of Pareto Distributions

Jagdish Saran, Kamal Nain
Pages: 259 - 272
In this paper, we establish some recurrence relations for marginal and joint moment generating functions of generalized order statistics from a new class of Pareto distributions. For a particular case these results verify the corresponding results of Athar et al. (2012).
Research Article

Efficient Rotation Pattern in Two-Phase Sampling

A. Bandyopadhyay, G.N. Singh
Pages: 261 - 268
The present investigation is an attempt to estimate the population mean on current occasion in two-phase successive (rotation) sampling over two occasions. Utilizing information on two auxiliary variables one chain-type estimator has been proposed to estimate the population mean on the current occasion....
Research Article

On Inference about Tilt Parameter in Marshall-Olkin Family of Distributions

Mostafa Tamandi
Pages: 261 - 270
Marshall and Olkin [Biometrika199784641652] introduced a method for constructing a new distribution by adding a new parameter, called tilt parameter, to a parent distribution. It is observed that adding this parameter leads to a more flexible model than the parent model. In this paper, different estimators...
Research Article

Properties of Shannon Entropy for Double Truncated Random Variables and its Applications

Rajesh Moharana, Suchandan Kayal
Pages: 261 - 273
Doubly truncated data are sometimes encountered in several applications, mainly in survival and astronomical data analysis. This occurs when the data falls between two points. In this study, we focus on the Shannon entropy measure of doubly truncated random variables. We propose ordering and various...
Research Article

Interactive Linear Models in Survey Sampling

Bikas K. Sinha, Pulakes Maiti
Pages: 263 - 272
Considered is a linear ‘interactive’ model in the context of survey sampling. This situation arises when investigator and/or supervisor interventions are contemplated in the responses. An appropriate linear model is introduced to represent the response profile(s) arising out of each respondent-cum-investigator-cum-supervisor...
Research Article

A Lifetime Distribution Based on a Transformation of a Two-Sided Power Variate

Mustafa C. Korkmaz, Ali I. Genc
Pages: 265 - 280
We introduce a new generalization of Weibull distribution by making use of a transformation of the standard two- sided power distributed random variable. Weibull and the exponentiated Weibull distributions are submodels of this new distribution.We show that this newly defined distribution is in fact...
Research Article

Planning Accelerated Life Tests for Burr Type X Failure Model with Type I Censoring

Nesar Ahmad, Sabiha Khan, M.G.M. Khan
Pages: 266 - 287
In this paper, we discuss the optimal accelerated life test plans for Burr type X distribution with log-linear model under periodic inspection and Type I censoring. We obtain the maximum likelihood estimators, the Fisher information and the asymptotic covariance matrix of the maximum likelihood estimators....
Research Article

An Alternative Approach of Binomial and Multinomial Distributions

Mian Arif Shams Adnan, Md. Tareq Ferdous Khan, Md. Forhad Hossain, Abdullah Albalawi
Pages: 269 - 283
In this paper we have tried to present an alternative approach for two discrete distributions such as Binomial and Multinomial with a new concept of sampling having a more general form apart from the traditional methods of sampling. The existing distributions may be obtained as a special case of our...
Research Article

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...
Research Article

A New Test for Simple Tree Alternative in a 2 x k Table

Parthasarathi Chakrabarti, Uttam Bandyopadhyay
Pages: 271 - 282
This paper considers simple tree order restriction in 2×k cohort study and provides a consistent test in which the usual multiple comparison test statistics are modified by using the characteristic roots of a consistent estimator of the associated correlation matrix. The relevant performance measures...

RETRACTED: Moment Generating Functions of Generalized Order Statistics From Extended Type II Generalized Logistic Distribution

Devendra Kumar
Pages: 273 - 288
This article has been retracted: please see the Atlantis Press Policy on Article Retraction and Withdrawal (

Research Article

The Alpha-Logarithmic Series Distribution of Order

C. Satheesh Kumar, A. Riyaz
Pages: 273 - 285
Here we develop an order k version of the alpha-logarithmic series distribution of Kumar and Riyaz (South African Statist. J., 2014) through its probability generating function and derive its probability mass function, mean and variance. The parameters of the model are estimated by the method...
Research Article

The Exponentiated Poisson-Exponential Distribution: A Distribution with Increasing, Decreasing and Bathtub Failure Rate

Francisco Louzada, Vicente G. Cancho, Paulo H. Ferreira
Pages: 274 - 285
In this paper we propose a new three-parameters lifetime distribution with increasing, decreasing and bathtub failure rate depending on its parameters. The properties of the proposed distribution are discussed, including explicit algebraic formulae for its reliability and failure rate functions, quantiles...
Research Article

The Odd Log-Logistic Geometric Family with Applications in Regression Models with Varying Dispersion

Maria do Carmo S. Lima, Fábio Prataviera, Edwin M. M. Ortega, Gauss M. Cordeiro
Pages: 278 - 294
We obtain some mathematical properties of a new generator of continuous distributions with two additional shape parameters called the odd log-logistic geometric family. We present some special models and investigate the asymptotes and shapes. The family density function can be expressed as a linear combination...
Research Article

Approach of Reliability Approximation with Extent of Error for a Resistor under Weibull Setup

Sadananda Nayak, Dilip Roy
Pages: 281 - 288
Analytical determination of reliability of a complex system is item dependent and setup dependent and a very difficult task. In this paper we propose reliability approximation based on reliability bounds for one such engineering item - a Resistor with independent components having the Weibull distribution....
Research Article

Generalized Semi Exponential Type Estimator under Systematic Sampling

Muhammad Nouman Qureshi, Sadia Khalil, Muhammad Hanif
Pages: 283 - 290
In sample surveys, collection of auxiliary information together with the main variable of interest is very important to increase the efficiency of the estimators of population parameters of interest. Regression and ratio estimation are very popular and are widely used methods that benefit from the use...
Research Article

On Records in Sequences of Nonidentically Distributed Exponential Random Variables

M. Ahsanullah, V.B. Nevzorov
Pages: 284 - 287
The representation of record values based on sequences of non-identically distributed exponential random variables in terms of independent exponential summands is suggested.
Research Article

A Note on Kumaraswamy Exponentiated Rayleigh distribution

Nasr Ibrahim Rashwan
Pages: 286 - 295
In this paper, a new four parameter continuous distribution, called the Kumaraswamy Rayleigh (KW-ER) distribution is proposed and studied. Some mathematical properties are presented and discussed, these properties involve expansions for the cumulative and density functions, skewness and kurtosis based...
Research Article

On the Probabilistic Latent Semantic Analysis Generalization as the Singular Value Decomposition Probabilistic Image

Pau Figuera Vinué, Pablo García Bringas
Pages: 286 - 296
The Probabilistic Latent Semantic Analysis has been related with the Singular Value Decomposition. Several problems occur when this comparative is done. Data class restrictions and the existence of several local optima mask the relation, being a formal analogy without any real significance. Moreover,...
Research Article

The Burr X Generator of Distributions for Lifetime Data

Haitham M. Yousof, Ahmed Z. Afify, G. G. Hamedani, Gokarna Aryal
Pages: 288 - 305
In this paper, we introduce a new class of distributions called the Burr X family. Some of its mathematical and structural properties are derived. The maximum likelihood is used for estimating the model parameters. The importance and flexibility of the new family are illustrated by means of an application...
Research Article

Quantile regression in high-dimension with breaking

Gabriela Ciuperca
Pages: 288 - 305
The paper considers a linear regression model in high-dimension for which the predictive variables can change the influence on the response variable at unknown times (called change-points). Moreover, the particular case of the heavy-tailed errors is considered. In this case, least square method with...
Research Article

Goodness-of-fit tests for weibull populations on the basis of records

Mahdi Doostparast
Pages: 289 - 300
Record is used to reduce the time and cost of running experiments (Doostparast and Balakrishnan, 2010). It is important to check the adequacy of models upon which inferences or actions are based (Lawless, 2003, Chapter 10, p. 465). In the area of goodness of fit based on record data, there are a few...
Research Article

A Generalization of Discounted Central Limit Theorem and its Berry-Esseen Analogue

B. Amiri Aghbilagh, Z. Shishebor, M.M. Saber
Pages: 289 - 295
Discounted central limit theorem was proved for i.i.d. random variables by Gerber (Theorem 2.1). This work is intended to extend the work of Gerber to the case where {??} is a periodic sequence of independent variables and ?i are periodic scalars. A simulation study was performed in order to support...
Research Article

Performance of the Graybill–Deal Estimator via Pitman Closeness Criterion

Keyu Nie, Bikas.K. Sinha, A.S. Hedayat
Pages: 291 - 306
Pitman closeness criterion is a coverage probability-based criterion to examine the relative performances of estimators. Usually, the performance of the standard Graybill-Deal estimator of the common mean has been examined with respect to the mean squared error (variance). In this study we examine its...
Research Article

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...
Research Article

Three parameter Transmuted Rayleigh distribution with application to Reliability data

Muhammad Shuaib Khan, Robert King, Irene Lena Hudson
Pages: 296 - 312
This research introduces the three parameter transmuted Rayleigh distribution with an application to fatigue fracture data. Using the quadratic rank transmutation map method proposed by Shaw et al. [25] we develop the three parameter transmuted Rayleigh distribution. This research also introduces the...
Research Article

Modified Clopper-Pearson Confidence Interval for Binomial Proportion

Desale Habtzghi, Chand K. Midha, Ashish Das
Pages: 296 - 310
We introduce expected coverage probability as a measure for constructing confidence intervals for the binomial proportion, p. We propose a model based confidence interval for p using the expected coverage probabilities of the Clopper-Pearson interval. The method provides intervals comparable or better...
Research Article

Exponentiated Power Function Distribution: Properties and Applications

Muhammad Zeshan Arshad, Muhammad Zafar Iqbal, Munir Ahmad
Pages: 297 - 313
In this study, we have focused to propose a flexible model that demonstrates increasing, decreasing and upside-down bathtub-shaped density and failure rate functions. The proposed model refers to as the exponentiated power function (EPF) distribution. Some mathematical and reliability measures are developed...
Research Article

Conditional risk estimate for functional data under strong mixing conditions

Abbes Rabhi, Sara Soltani, Aboubacar Traore
Pages: 301 - 323
We consider the problem of nonparametric estimation of the conditional hazard function for functional mixing data. More precisely, given a strictly stationary random variables Zi = (Xi; Yi)i2N, we investigate a kernel estimate of the conditional hazard function of univariate response variable Yi given...
Research Article

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...
Research Article

Bonferroni and Gini Indices and Recurrence Relations for Moments of Progressive Type-II Right Censored Order Statistics from Marshall-Olkin Exponential Distribution

Narinder Pushkarna, Jagdish Saran, Rashmi Tiwari
Pages: 306 - 320
In this paper, we derive explicit expressions for Bonferroni Curve (BC), Bonferroni index (BI), Lorenz Curve (LC) and Gini index (GI) for the Marshall-Olikn Exponential (MOE) distribution, which have mainly concern with some aspects like poverty, welfare, decomposability, reliability, sampling and inference.We...
Research Article

Some Results on Stochastic Orderings of Generalized Order Statistics and Spacings

Z. Zamani, G. R. Mohtashami Borzadaran, M. Amini
Pages: 306 - 321
Generalized order statistics unify the study of order statistics, record values, k-records, Pfeifer’s records and several other cases of ordered random variables. In this paper, we first provide several comparison results for generalized order statistics in terms of the dynamic cumulative residual quantile...