Journal of Statistical Theory and Applications

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253 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...

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 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 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...

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....

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...

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...

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...

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),...

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...

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,...

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.

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...

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...

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,...

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...

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...

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...

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...

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...

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....

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...

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...

Characterizations of probability distributions via bivariate regression of generalized order statistics

M.S. Kotb, M. Ahsanullah
Pages: 321 - 329
Let Xi,n,m,k, i = 1, ...,n are n generalized order statistics (gos) based on an absolutely continuous distribution function F. Suppose that ? (x) is an absolutely continuous and monotonically increasing function in (a,b), ???a

The Log-Beta Generalized Half-Normal Regression Model

Rodrigo R. Pescim, Edwin M.M. Ortega, Gauss M. Cordeiro, Clarice G.B. Demtrio, G.G. Hamedani
Pages: 330 - 347
We introduce a log-linear regression model based on the beta generalized half-normal distribution (Pescim et al., 2010).We formulate and develop a log-linear model using a new distribution so-called the log-beta general- ized half normal distribution.We derive expansions for the cumulative distribution...

Wrapped Geometric Distribution: A new Probability Model for Circular Data

Sophy Jacob, K. Jayakumar
Pages: 348 - 355
We propose a new family of circular distributions, obtained by wrapping geometric distribution on Z+ = 0, 1, . . ., around a unit circle. The properties of this new family of distributions are studied.

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

M. Maswadah, Ali M. Seham, M. Ahsanullah
Pages: 356 - 377
In this paper, the confidence intervals for the generalized gamma distribution parameters are derived based on the Bayesian approach using the informative and non-informative priors and the classical approach, via the Asymptotic Maximum likelihood estimation, based on the generalized order statistics....

Beta-Cauchy Distribution: Some Properties and Applications

Etaf Alshawarbeh, Felix Famoye, Carl Lee
Pages: 378 - 391
Some properties of the four-parameter beta-Cauchy distribution such as the mean deviation and Shannon’s entropy are obtained. The method of maximum likelihood is proposed to estimate the parameters of the distribution. A simulation study is carried out to assess the performance of the maximum likelihood...

Interval Mapping Using Nonparametric Accelerated Failure Time Cure Model

Devrim Bilgili, Nader Ebrahimi
Pages: 392 - 402
Many important problems in evolutionary biology begin with observations of phenotypic variation. Suppose time to an event-data are used to map quantitative trait loci (QTL) and underlying population is a mixture of susceptible and non-susceptible subjects. If the cured subjects are ignored we may fail...

Assessment of Non-Response under Ratio Method of Imputation in Two- Occasion Successive Sampling

G.N. Singh, D. Majhi, S. Prasad, F. Homa
Pages: 403 - 418
This paper considers the problem of estimation of the population mean of the study character under ratio method of imputation when some observations in the sample data are missing at random and the information on an auxiliary variable is readily available on both the occasions in two-occasion successive...

Bayesian Estimation in Some Power Series Distributions

Anwar Hassan, Peer Bilal Ahmad, Anwar H. Joarder
Pages: 419 - 427
In this paper, we study the Bayesian estimation of functions of parameters of some power series distributions. These estimators are better than the classical minimum variance unbiased estimators (MVUE) as given by Patil and Joshi (1970), in the sense that these increase the range of the estimation 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 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.

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...

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...

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...

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...

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,...

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...

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...

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...

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.

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...

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.

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...

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...

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...

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.