Journal of Statistical Theory and Applications

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262 articles

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....

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...

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.

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...

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...

Generalized Sichel Distribution and Associated Inference

Yeh Ching Low, Seng Huat Ong, Ramesh C. Gupta
Pages: 322 - 336
In this paper, we propose a generalized form of Sichel distribution which is obtained by mixing the Poisson distribution with the extended generalized inverse Gaussian distribution. This distribution models over dispersed, zero-inflated and heavy-tailed count data sets. These characteristics are examined...

Least Squares Parameter Estimation for Sparse Functional Varying Coefficient Model

Behdad Mostafaiy, Mohammad Reza Faridrohani
Pages: 337 - 344
In the present paper, we study functional varying coefficient model in which both the response and the predictor are functions. We give estimates of the intercept and the slope functions in the case that the observations are sparse and noise-contaminated longitudinal data by using least squares representation...

Improved Confidence Intervals for the Ratio of Coefficients of Variation of Two Lognormal Distributions

Md Sazib Hasan, K. Krishnamoorthy
Pages: 345 - 353
The problem of estimating the ratio of coefficients of variation of two independent lognormal populations is considered. We propose two closed-form approximate confidence intervals (CIs), one is based on the method of variance estimate recovery (MOVER), and another is based on the fiducial approach....

Slashed Moment Exponential Distribution

Yuri A. Iriarte, Juan M. Astorga, Osvaldo Venegas, Héctor W. Gómez
Pages: 354 - 365
The problem of estimating the ratio of coefficients of variation of two independent lognormal populations is considered. We propose two closed-form approximate confidence intervals (CIs), one is based on the method of variance estimate recovery (MOVER), and another is based on the fiducial approach....

Large Sample Inference about the Ratio of Means in Two Independent Populations

Mohammad Reza Mahmoudi, Javad Behboodian, Mohsen Maleki
Pages: 366 - 374
In a number of situations, for example in biology, psychology and neurosciences, researchers are interested in the ratio of two measured quantities. In this paper, we give an overview of different methods to constructing confidence limits for the ratios. Then by using the limiting theorems, a pivotal...

Tail dependence coefficient of generalized hyperbolic distribution

Mohalilou Aleiyouka, Alexandre Berred, Mohammad Ahsanullah
Pages: 375 - 381
The tail dependence describes the limiting proportion of exceeding one margin over a certain threshold given that the other margin has already exceeded that threshold. In this paper, we obtain the limit tail dependence coefficient for the generalized hyperbolic distribution.

The Odd Log-Logistic Marshall-Olkin Lindley Model for Lifetime Data

Morad Alizadeh, Gamze Ozel, Emrah Altun, Mousa Abdi, G.G. Hamedani
Pages: 382 - 400
A new three parameter model called the odd log-logistic Marshall-Olkin-Lindley (OLLMO-L) distribution is proposed and studied. This distribution is symmetric, platykurtic, leptokurtic and unimodal. Various structural properties are derived, including explicit expressions for the ordinary and conditional...

The new family of distributions and applications in heteroscedastic regression analysis

Gauss M. Cordeiro, Thiago G. Ramires, Edwin M.M. Ortega, Morad Alizadeh
Pages: 401 - 418
First we introduce and study some general mathematical properties of a new generator of continuous distributions with two extra shape parameters called the odd generalized half-Cauchy family. A second goal, we introduce the new log-generalized odd half-Cauchy heteroscedastic regression model with censored...

Some Inferences on Skew-t Distribution of 2 Degrees of Freedom

Mohammad Ahsanullah, Valery B. Nevzorov
Pages: 419 - 426
Understanding the properties of Skew distributions is important in many statistical applications. The Student-t distribution is widely used in statistics. Skew-t distribution is a useful model to describe data with heavy tails. In this paper several distributional properties of Skew-t distribution are...

The Marshall-Olkin-Kumaraswamy-G family of distributions

Laba Handique, Subrata Chakraborty, G.G. Hamedani
Pages: 427 - 447
A new family of continuous probability distributions is proposed by using Kumaraswamy-G distribution as the base line distribution in the Marshall-Olkin construction. A number of known distributions are derived as particular cases. Various properties of the proposed family like formulation of the pdf...

A New Four-ParameterWeibull Model for Lifetime Data

Haitham M. Yousof, Ahmed Z. Afify, Gauss M. Cordeiro, Ayman Alzaatreh, Mohammad Ahsanullah
Pages: 448 - 466
We introduce a new four-parameter distribution with constant, decreasing, increasing, bathtub and upside-down bathtub failure rate called the transmuted exponentiated generalized Weibull model. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments,...

Interactive Linear Models in the Context of Two-Stage Sampling

Pulakesh Maiti
Pages: 467 - 475
We study an interactive linear model that incorporates investigator and/or supervisor interventions in the context of a two-stage sampling design. We obtain an unbiased estimator of the finite population total and derive an unbiased estimator of its variance. Our method builds on Sinha and Maiti (2014),...

Efficient Utilization of Auxiliary Information on Estimation of Population Mean Using Exponential Type Estimators in Successive Sampling

Surya K. Pal, Housila P. Singh
Pages: 476 - 489
This paper advocates the problem of estimating the population mean on the current occasion in two occasion successive (rotation) sampling under the transformed auxiliary variable using exponential method of estimation. Four different type estimators are suggested for estimating the current population...

A new family of distributions to analyze lifetime data

M. Mansoor, M. H. Tahir, Gauss M. Cordeiro, Ayman Alzaatreh, M. Zubair
Pages: 490 - 507
In this paper, a new family of distributions is proposed by using quantile functions of known distributions. Some general properties of this family are studied. A special case of the proposed family is studied in detail, namely the Lomax-Weibull distribution. Some structural properties of the special...

On the Assessment of Average Biosimilarity Based on a Three-Arm Parallel Design

Ginto Jacob Pottackal, Thomas Mathew
Pages: 508 - 521
Average biosimilarity is investigated under a three-arm parallel design: one arm corresponds to the test drug T , and the other two arms correspond to two versions of the reference drug, say R1 and R2. The hypothesis of interest is the equivalence of the population average response for T with the mean...

A New Generalization of Weighted Geometric Distribution and its Properties

H. Najarzadegan, M. H. Alamatsaz
Pages: 522 - 546
Discrete distributions are widely used to model lifetime for count data. In this paper we introduce a new generalization of weighted geometric (GWG) distribution with the weight function w(x) = (1−p^{αx})^β whose special case proposes a discrete generalized weighted exponential distribution. Further,...

The Log-gamma-logistic Regression Model: Estimation, Sensibility and Residual Analysis

Elizabeth M. Hashimoto, Edwin M.M. Ortega, Gauss M. Cordeiro, G.G. Hamedani
Pages: 547 - 564
In this paper, we formulate and develop a log-linear model using a new distribution called the log-gammalogistic. We show that the new regression model can be applied to censored data since it represents a parametric family of models that includes as sub-models several widely-known regression models...

A Class of Exponential Regression Type Estimators for Population Variance in Two-Phase Sampling

A. Chatterjee, G.N. Singh, A. Bandyopadhyay
Pages: 565 - 575
This article deals with the problems of efficient estimation of population variance in two-phase (double) sampling. Using information on two auxiliary variables, a class of chain exponential to regression type estimators has been proposed and its properties are studied under two different structures...

A New Quasi Poison-Lindley Distribution: Properties and Applications

Munindra Borah, Junali Hazarika
Pages: 576 - 588
A new two parameter quasi Poisson Lindley (NQPL) distribution is derived by using the general approach of compounding. One parameter Lindley distribution and geometric distribution may be obtained as a particular case. The new distribution is shown to be unimodal and overdispersed. A few distributional...

Comparing the Fisher information matrix in record values and random observations for the general class of exponentiated distributions

Fatih Kızılaslan
Pages: 589 - 604
In this paper, the Fisher information matrix (FIM) contained in n record values is considered for the two parameter distributions belong to the exponentiated and inverse exponentiated class of distributions. The problem of existence and uniqueness of the maximum likelihood estimates of the parameters...

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...

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...

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...

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,...

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...

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,...

Combined Intra- and Inter- Block Analysis of Balanced Ternary Designs

Sobita Sapam, B. K. Sinha, N.K. Mandal
Pages: 91 - 100
In the present paper an attempt has been made to study the inter–and intra-block estimation of treatment effects contrasts with random block effects in the context of balanced ternary designs. The analysis is illustrated through examples.

On Some Aspects of a New Class of Two-Piece Asymmetric Normal Distribution

C. Satheesh Kumar, M.R. Anusree
Pages: 101 - 121
Through this chapter, we introduce a new class of two-piece asymmetric normal distribution suitable for asymmetric and plurimodal situations. We study some important aspects of this distribution by deriving explicit expressions for its distribution function, characteristic function, reliability measures...

Estimating the parameters of Lomax distribution from imprecise information

Abbas Pak, Mohammad Reza Mahmoudi
Pages: 122 - 135
Traditional statistical approaches for estimating the parameters of Lomax distribution have dealt with precise information. However, in real world situations, some information about an underlying system might be imprecise and are represented in the form of fuzzy information. In this paper, we consider...

Estimating Quantiles of Two Exponential Populations with a Common Location Parameter Using Censored Samples

Adarsha Kumar Jena, Manas Ranjan Tripathy
Pages: 136 - 145
Estimation of quantiles of two exponential populations is considered assuming equality of location parameters using censored samples from a decision theoretic point of view. Sufficient conditions for inadmissibility of estimators in certain classes have been derived. Consequently some complete class...

Bayesian Inference Based on Multiply Type-II Censored Sample from a General Class of Distributions

A.R. Shafay, M.M. Mohie El-Din, Y. Abdel-Aty
Pages: 146 - 157
In this paper, we consider a general form for the underlying distribution and a general conjugate prior, and develop a general procedure for Bayesian estimation based on an observed multiply Type-II censored sample. The problem of predicting the order statistics from a future sample are also discussed...

Divergence Measures Estimation and Its Asymptotic Normality Theory Using Wavelets Empirical Processes I

Amadou Diadié Ba, Gane Samb LO, Diam Ba
Pages: 158 - 171
We deal with the normality asymptotic theory of empirical divergences measures based on wavelets in a series of three papers. In this first paper, we provide the asymptotic theory of the general of ϕ-divergences measures, which includes the most common divergence measures : Renyi and Tsallis families...

On Some Aspects of Strong Risk Class and Associated Ordering

Mervat Mahdy
Pages: 172 - 192
The paper opens up a new aging class and a new stochastic orders which is depend on risk class, that plays vital role in the reliability theory, finance topics, stochastic orders, and the economic theory. The article presents some new interesting implications and characterizations concerning this class....

On Evolution of Statistical Inference

DAS Fraser
Pages: 193 - 205
The foundations of statistics have evolved over many centuries, perhaps millennia, with major paradigm shifts of the form described in Kuhn (1962). We briefly consider these important transitions and how they have led to major shifts in the foundations of statistical inference. Clearly there is no conventional...

Record Ranges for Samples From Asymmetrical Laplace Distributions

Pages: 206 - 212
The representations of record ranges via sums of independent identically distributed exponential random variables are obtained for asymmetrical Laplace distributions. This result generalizes the corresponding relations for record values in the cases of exponential and negative exponential distributions

The Extended Exponential Distribution and Its Applications

Ahmed Z. Afify, Mohamed Zayed, Mohammad Ahsanullah
Pages: 213 - 229
We introduce a new three-parameter extension of the exponential distribution called the odd exponentiated half-logistic exponential distribution. Various of its properties including quantile and generating functions, ordinary and incomplete moments, mean residual life, mean inactivity time and some characterizations...

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...

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...

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...

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...

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...

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...

A Tutorial on Levels of Granularity: From Histograms to Clusters to Predictive Distributions

Pages: 307 - 323
Consider the problem of modeling datasets such as numbers of accidents in a population of insured persons, or incidences of an illness in a population. Various levels of detail or granularity may be considered in describing the parent population. The levels used in fitting data and hence in describing...

A class of Bivariate SURE estimators in heteroscedastic hierarchical normal models

S.K. Ghoreishi
Pages: 324 - 339
In this paper, we first propose a class of bivariate shrinkage estimators based on Steins unbiased estimate of risk (SURE). Then, we study the effect of correlation coefficients on their performance. Moreover, under some mild assumptions on the model correlations, we set up the optimal asymptotic properties...

Joint Modeling of Linear Degradation and Multiple Dependent Competing Risks Data under a Step-Stress Accelerated Degradation Test

Somayeh Mireh, Ahmad Khodadadi, Firoozeh Haghighi
Pages: 340 - 358
The step-stress accelerated degradation test (SSADT) is one of the most commonly used time-dependent types of stress loading tests that enables a shorter test duration. This test is more economical and flexible compared to accelerated degradation test or accelerated failure time (ADT/AFT) test plans....