Journal of Statistical Theory and Applications

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263 articles

Augmented Strength Reliability of Equipment Under Gamma Distribution

N. Chandra, Subhradev Sen
Pages: 212 - 221
The strength-reliability of equipment is defined as the probability that the strength of the equipment exceeds its stress. Augmentation of strength-reliability of equipments gives better service protection and longevity. In this paper, the concept of Augmentation Strategy Plan (ASP) is introduced under...

Characterizations of a Class of Distributions by Dual Generalized Order Statistics and Truncated Moments

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....

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...

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...

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...

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...

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...

Characterizations of distributions via record values with random exponential shifts

Mohammad Ahsanullah, Valery B. Nevzorov, Ludmila Nevzorova
Pages: 311 - 316
Some new characterizations of probability distributions based on properties of record values shifted by independent exponential variables are obtained. Explicit expressions for the inverse functions of the corresponding variables are presented. Among others some characterizations of exponential distributions...

A Bayesian Shared Parameter Model for Incomplete Semicontinuous longitudinal Data: An Application To Toenail Dermatophyte Onychomycosis Study

Samaneh Eftekhari Mahabadi
Pages: 317 - 332
Most of statistical analysis for longitudinal data are based on normality assumption for the continuous response of interest which might be violated in some practical areas due to skewed data which possibly contain excess zeros. Some authors have proposed frequentist and Bayesian approaches to model...

Estimation of Population Mean Using Known Correlation Coefficient And Median

J. Subramani, G. Kumarapandiyan
Pages: 333 - 343
The present paper deals with the two modified ratio estimators for estimation of population mean of the study variable using the linear combination of the known population values of the Correlation Coefficient and the Median of the auxiliary variable. The biases and the mean squared errors of the proposed...

On Finite Mixtures of Modified Intervened Poisson Distribution And Its Applications

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...

Nonparametric Estimation of the Interval Reliability

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...

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...

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...

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...

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.

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...

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...

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...

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...

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...

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.

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...

Bayesian test of independence and conditional independence of two ordinal variables

Zahra Saberi, Mojtab Ganjali
Pages: 156 - 168
For analysis of contingency tables with large sample size, classical approaches using approximate methods have high power. However, when the sample size is small or some cells have frequencies less than 5, classical approaches are so conservative. Also asymptotic behavior may be poor when the table contains...

On the Weibull-X family of distributions

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...

Expectation Identities of Generalized Order Statistics from Marshall-Olkin Extended Uniform Distribution and its Characterization

Haseeb Athar, Nayabuddin
Pages: 184 - 191
The Marshall-Olkin extended uniform distribution is introduced and studied by Jose and Krishna (2011). In this paper some moments properties of generalized order statistics (gos) for this distribution are investigated and results are deduced for order statistics and record values. In the last section,...

Estimating Per Capita Rates Using Aggregate Measurements From Groups of Diverse Compositions

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...

Shrinkage estimates for multi-level heteroscedastic hierarchical normal linear models

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...

Study of Dual to Ratio-Cum-Product Estimator of Finite Population Mean under Double Sampling in Sample Surveys

Sanjib Choudhury, Bhupendra Kumar Singh
Pages: 214 - 221
A class of estimator based on dual to ratio and dual to product-type estimator in double sampling for estimating finite population mean is proposed. The bias and mean square error of the proposed estimator are obtained in two different cases. A comparative study has been made with usual estimators, dual...

The Kumaraswamy-G Poisson Family of Distributions

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 distributions...

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...

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

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...

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....

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...

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...

Estimation of the Parameters of a Bivariate Geometric Distribution

U.J. Dixit, S. Annapurna
Pages: 324 - 349
The uniformly minimum variance unbiased estimators (UMVUE) of the parameters and reliability functions of a bivariate geometric distribution(BGD) have been derived.The exact variances of the maximum likelihood estimator (MLE) and of UMVUE have been derived and the corresponding mean square errors have...

Characterizations of Distributions Via Conditional Expectation of Function of Generalized Order Statistics

Mohammad Ahsanullah, G.G. Hamedani, Indranil Ghosh
Pages: 350 - 358
Characterizations of probability distributions by different regression conditions on generalized order statistics have attracted the attention of many researchers. We present here, characterization of distributions based on the conditional expectation of generalized order statistics extending the characterization...

On Hilbert

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 covariance...

A Weibull Generated Exponentiated Exponential Model: Properties and Bayes Interval Prediction

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 of...

Likelihood-based inference for the power half-normal distribution

Yolanda M. Gómez, Heleno Bolfarine
Pages: 383 - 398
In this paper we consider an extension of the half-normal distribution based on the distribution of the maximum of a random sample. It is shown that this distribution belongs to the family of beta generalized half-normal distributions. Properties of its density are investigated, maximum likelihood estimation...

Dynamic Cumulative Residual and Past Inaccuracy Measures

Vikas Kumar, H.C. Taneja
Pages: 399 - 412
In this paper, we have developed measures of dynamic cumulative residual and past inaccuracy. We have studied characterization results under proportional hazard model in case of dynamic cumulative residual inaccuracy and under proportional reversed hazard model in case of dynamic cumulative past inaccuracy...

Correlation Based Ridge Parameters in Ridge Regression with Heteroscedastic Errors and Outliers

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...

Some Generalizations of Weibull Distribution and Related Processes

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...

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,...

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...

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...

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...