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...

Gane Samb Lo, El Hadji Deme, Aliou Diop

Pages: 21 - 38

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...

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...

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)...

Angel Mathew, N. Balakrishna

Pages: 356 - 366

The interval reliability of a repairable system is the probability that the system is operating at a specified time and
will continue to operate for a specified interval of time. This quantity is especially important for equipment, which
must be working when an emergency situation arises. The present...

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...

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.

Ayman Alzaatreh, Indranil Ghosh

Pages: 169 - 183

In this paper, the Weibull-X family is proposed and some of its properties are discussed. A member of the
Weibull-X family, the Weibull-logistic distribution, is defined and studied. Various properties of the Weibulllogistic
distribution are obtained. The distribution is found to be unimodal and the...

Donald N. Stengel, Priscilla Chaffe-Stengel

Pages: 192 - 203

This paper considers the problem of estimating a variable mean for a population of elements where data are only available as aggregate sums for groups of multiple elements. The proposed model addresses an additional complication created when the group measure includes the contribution of diverse elements...

S.K. Ghoreishi, A. Mostafavinia

Pages: 204 - 213

Empirical Bayes approach is an attractive method for estimating hyperparameters in hierarchical models. But,
under the assumption of normality for a multi-level heteroscedastic hierarchical model, which involves several
explanatory variables, the analyst may often wonder whether the shrinkage estimators...

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....

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...

Miroslav M. Ristić

Pages: 206 - 206

A.V. Dorugade

Pages: 413 - 424

This paper introduces some new estimators for estimating ridge parameter, based on correlation between response
and regressor variables for ridge regression analysis. A simulation study has been made to evaluate the performance
of proposed estimators based on the minimum mean squared error (MSE) criterion...

Ahmed Z. Afify, Haitham M. Yousof, G.G. Hamedani, Gokarna R. Aryal

Pages: 326 - 344

A new generalization of the Weibull-Pareto distribution called the exponentiated Weibull-Pareto distribution is
defined and studied. Various structural properties including ordinary moments, quantiles, R´enyi and q-entropies
and order statistics are derived. We proposed the method of maximum likelihood...

Rahul Bhattacharya

Pages: 400 - 404

For testing a simple null hypothesis against a simple alternative using Neyman-Pearson theory, examples of
most powerful non-randomized critical regions are constructed, which are overlapping for varying sizes. A
likelihood ratio based criterion, characterizing such critical regions, is also provided....

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...

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...

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,...

Saeid Tahmasebi, Maryam Eskandarzadeh, Ali Akbar Jafari

Pages: 165 - 177

In this paper, a new extension of cumulative residual entropy is proposed. It contain the generalized cumulative residual entropy introduced by Psarrakos and Navarro (2013) and is related with the k-record values. We also consider a dynamic version of this new cumulative residual entropy using the residual...

Eisa Mahmoudi, Hamed Mahmoodian

Pages: 198 - 208

Recently, Mahmoudi and Mahmoodian [7] introduced a new class of distributions which contains univariate normal–geometric distribution as a special case. This class of distributions are very flexible and can be used quite effectively to analyze skewed data. In this paper we propose a new bivariate distribution...

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...

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...

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...

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...

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...

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....

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...

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...

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.

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...

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....

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...

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...

Filippo Domma, G.G. Hamedani

Pages: 222 - 234

The problem of characterizing a distribution is an important problem which has recently attracted the attention
of many researchers. Thus, various characterizations have been established in many different directions. The
present work deals with the characterizations of a general class of distributions....

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...

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...

Devendra Kumar

Pages: 273 - 288

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 generalized logistic distribution. Further the results are deduced for moments of ?kth record values and ordinary order...

C. Satheesh Kumar, D.S. Shibu

Pages: 344 - 355

Kumar and Shibu proposed a modified version of intervened Poisson distribution (IPD), namely the modified intervened Poisson
distribution (MIPD) for tackling situations of further interventions useful for certain practical problems. Here we consider some
finite mixtures of MIPD and study some of its...

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...

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...

Manoel Wallace A. Ramos, Pedro Rafael D. Marinho, Gauss M. Cordeiro, Ronaldo V. da Silva, G.G. Hamedani, Joao Pessoa

Pages: 222 - 239

For any baseline continuous G distribution, we propose a new generalized family called the Kumaraswamy-G
Poisson (denoted with the prefix “Kw-GP”) with three extra positive parameters. Some special distributions
in the new family such as the Kw-Weibull Poisson, Kw-gamma Poisson and Kw-beta Poisson...

K. Jayakumar, M. Girish Babu

Pages: 425 - 434

A new class of distributions containing Marshall-Olkin extended Weibull distribution is introduced. The role of this
distribution in the study of minification process is established. A new class of distributions that includes the
Laplace and Logistic distributions is introduced. Properties and generation...

K. Shafie

Pages: 359 - 367

In this paper random variables that take their values from a Hilbert *C**-module are defined and three definitions
for the mean, covariance operator, and Gaussian distribution of these random variables are given and it is
shown that these definitions are equivalent. Furthermore, the concept of...

Essam K. AL-Hussaini, Alaa H. Abdel-Hamid

Pages: 368 - 382

Motivated by the fact that the so-called Weibull generated exponentiated exponential distribution (WGEED)
accommodates for non-monotone as well as monotone hazard rate functions (HRFs), we give some properties of
this WGEED and explore its use in life testing by obtaining Bayes prediction intervals...

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...

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...

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
(*k*_{1}), structure (*k*_{2}) and structure (*k*_{1}*k*_{2}) properties of a factorial design. We establish properties of each...

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...