Journal of Statistical Theory and Applications

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293 articles
Research Article

Shrinkage Estimation of Linear Regression Models with GARCH Errors

S. Hossain, M. Ghahramani
Pages: 405 - 423
This paper introduces shrinkage estimators for the parameter vector of a linear regression model with con- ditionally heteroscedastic errors such as the class of generalized autoregressive conditional heteroscedastic (GARCH) errors when some of the regression parameters are restricted to a subspace....
Research Article

Characterizations of Exponential Distribution Based on Two-Sided Random Shifts

Santanu Chakraborty, George P. Yanev
Pages: 408 - 418
A new characterization of the exponential distribution is obtained. It is based on an equation involving randomly shifted (translated) order statistics. No specific distribution is assumed for the shift random variables. The proof uses a recently developed technique including the Maclaurin series expansion...
Research Article

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...
Research Article

Generalized Exponential Estimator for the Estimation of Clustered Population Variance in Adaptive Cluster Sampling

Muhammad Nouman Qureshi, Ayesha Iftikhar, Muhammad Hanif
Pages: 416 - 424
In this paper, we proposed a generalized exponential estimator with two auxiliary variables for the estimation of highly clumped population variance under adaptive cluster sampling design. The expressions of approximate bias and minimum mean square error are derived. A family of exponential ratio and...
Research Article

Shannon Information in K-records for Pareto-type Distributions

Zohreh Zamani, Mohsen Madadi
Pages: 419 - 438
Pareto distributions provides models for many applications in the social, natural and physical sciences. In this paper, we derive the Shannon information contained in upper (lower) k-record values and associated k-record times of Pareto-type distributions for a finite sample of fixed size and for an...
Research Article

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...
Research Article

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...
Research Article

Diagnostics of a Multiresponse Regression Model with Autocorrelated Errors

Sibnarayan Guria, Sugata Sen Roy
Pages: 424 - 433
In this paper we study the diagnostics of a multiresponse regression model with a first-order autoregressive error sequence. The deletion technique is used to identify the outliers taking account of the dependence structure of the errors. Besides the usual measures, some scalar measures to gauge the...
Research Article

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...
Research Article

Generalized Componentwise Splitting Scheme For Option Pricing Under The Heston-Cox-Ingersoll-Ross Model

Maryam Safaei, Abodolsadeh Neisy, Nader Nematollahi
Pages: 425 - 438
In this paper, we consider a numerical pricing of European call and put options under the Heston-Cox-Ingersoll-Ross (HCIR) model. Based on this model, the prices of options are derived by solving a three-dimensional partial differential equation. We generalize a componentwise splitting scheme for solving...
Research Article

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...
Research Article

Parameter Estimation Using the EM Algorithm for Symmetric Stable Random Variables and Sub-Gaussian Random Vectors

Mahdi Teimouri, Saeid Rezakhah, Adel Mohammadpour
Pages: 439 - 461
Applying some well-known properties of the class of symmetric α-stable (SαS) distribution, the EM algorithm is extended to estimate the parameters of SαS distributions. Furthermore, we extend this algorithm to the multivariate sub-Gaussian α-stable distributions. Some comparative studies are performed...
Research Article

A New F-Test Applicable to Large-Scale Data

Mohsen Salehi, Adel Mohammadpour, Kerrie Mengersen
Pages: 439 - 449
In large-scale multiple testing, the permutation test based on making a null statistic has been widely employed in the literature. Because it enables us to use the null permuted samples and estimate the p-value more accurately. Some test statistics, which can be modified to a null statistic, have been...
Research Article

A New Four-Parameter Weibull 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,...
Research Article

Analysis of Count Data by Transmuted Geometric Distribution

Subrata Chakraborty, Deepesh Bhati
Pages: 450 - 463
Transmuted geometric distribution (TGD) was recently introduced and investigated by Chakraborty and Bhati [Stat. Oper. Res. Trans. 40 (2016), 153–176]. This is a flexible extension of geometric distribution having an additional parameter that determines its zero inflation as well as the tail length....
Research Article

Active and Dynamic Approaches for Clustering Time Dependent Information: Lag Target Time Series Clustering and Multi-Factor Time Series Clustering

Doo Young Kim, Chris P. Tsokos
Pages: 462 - 477
One of data mining schemes in statistics is clustering panel data such as longitudinal data and time series data. Classical approaches to cluster such time dependent information do not properly count time dependencies among objects we are interested to analyze. In the present study, we propose an approach...
Research Article

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),...
Research Article

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...
Research Article

Generalized Poisson and Geometric Distributions – An Alternative Approach

Md. Tareq Ferdous Khan, Mian Arif Shams Adnan, Md. Forhad Hossain, Abdullah Albalawi
Pages: 478 - 490
An alternative approach of Poisson and Geometric distributions having a more general form of sampling method are suggested in this paper and defined them as generalized Poisson and generalized Geometric distributions respectively. It is evident that the traditional forms of both the distributions are...
Research Article

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...
Research Article

Parameter Estimation and Application of Generalized Inflated Geometric Distribution

Avishek Mallick, Ram Joshi
Pages: 491 - 519
A count data that have excess number of zeros, ones, twos or threes are commonplace in experimental studies. But these inflated frequencies at particular counts may lead to overdispersion and thus may cause difficulty in data analysis. So to get appropriate results from them and to overcome the possible...
Research Article

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...
Research Article

f-Majorization with Applications to Stochastic Comparison of Extreme Order Statistics

Esmaeil Bashkar, Hamzeh Torabi, Ali Dolati, Félix Belzunce
Pages: 520 - 536
In this paper, we use a new partial order, called f-majorization order. The new order includes as special cases the majorization, the reciprocal majorization and the p-larger orders. We provide a comprehensive account of the mathematical properties of the f-majorization order and give applications of...
Research Article

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,...
Research Article

Estimating the Parameters of a Generalized Exponential Distribution

Syed Afzal Hossain
Pages: 537 - 553
A three-parameter generalized exponential distribution was suggested by Hossain and Ahsanullah [5]. Some important aspects of this distribution in the area of estimation remain unexplored in the earlier works. We discuss here the maximum likelihood (ML) method and the method of moments to estimate the...
Research Article

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...
Research Article

The Exponential Lindley Odd Log-Logistic-G Family: Properties, Characterizations and Applications

Mustafa Ç. Korkmaz, Haitham M. Yousof, G. G. Hamedani
Pages: 554 - 571
A new family of distributions called the exponential Lindley odd log-logistic G family is introduced and studied. The new generator generalizes three newly defined G families and also defines two new G families. We provide some mathematical properties of the new family. Characterizations based on truncated...
Research Article

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...
Case Study

Modeling Pinhole Phenomenon in Sanitary Porcelains Case Study: Isatis Sanitary Porcelain Plant, Yazd, Iran

H. Bazargan, A. Dehghanzadeh
Pages: 572 - 586
Sanitary porcelain products might have several defects, causing potential high-grade desirable products be converted into low-grade ones. Some of the defects are such that a few of them in the products will result in a great fall of product rating and consequently reduction of its value and price. Among...
Research Article

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...
Research Article

On Time Series Analysis for Repeated Surveys

Mohamed A. Ismail, Hend A. Auda, Yehia Ahmed Elzafrany
Pages: 587 - 596
Governments and other agencies repeated many important surveys at regular time intervals, but the population mean is estimated mainly using the latest survey. Time series estimators for the population mean using repeated surveys are superior to those obtained from the last survey. This superiority may...
Research Article

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...
Research Article

Estimation of a Finite Population Proportion in Light of Randomized Reporting

Pulakesh Maiti, Jyotirmoy Sarkar, Bikas K. Sinha
Pages: 597 - 605
In large scale surveys, it is customary to accept unaltered the responses provided by the respondents, leaving no provision for investigators to pass on any circumstantial judgment on the responses. This restrictive practice sometimes vitiates the estimation of a parameter. Here we consider a real life...
Research Article

A Study of the First-Order Continuous-Time Bilinear Processes Driven by Fractional Brownian Motion

Abdelouahab Bibi, Fateh Merahi
Pages: 606 - 615
The continuous-time bilinear (COBL) process has been used to model non linear and/or non Gaussian datasets. In this paper, the first-order continuous-time bilinear COBL (1, 1) model driven by a fractional Brownian motion (fBm for short) process is presented. The use of fBm processes with certain Hurst...
Research Article

A Generalized Class of Estimators for Estimating Population Mean in the Presence of Non-Response

Iram Saleem, Aamir Sanaullah, Muhammad Hanif
Pages: 616 - 626
Koyuncu and Kadilar proposed an estimator based on single auxiliary variable with complete response in stratified random sampling. In this paper, we extended Koyuncu and Kadilar’s estimator to a more generalized class of estimators using two auxiliary variables in stratified random sampling for the situation...
Research Article

Interval-Valued Uncertainty Based on Entropy and Dempster–Shafer Theory

F. Khalaj, E. Pasha, R. Tavakkoli-Moghaddam, M. Khalaj
Pages: 627 - 635
This paper presents a new structure as a simple method at two uncertainties (i.e., aleatory and epistemic) that result from variabilities inherent in nature and a lack of knowledge. Aleatory and epistemic uncertainties use the concept of the entropy and Dempster–Shafer (D–S) theory, respectively. Accordingly,...
Research Article

Efficient Estimator of Parameters of a Multivariate Geometric Distribution

U. J. Dixit, S. Annapurna
Pages: 636 - 646
The maximum likelihood estimator (MLE) and uniformly minimum variance unbiased estimator (UMVUE) for the parameters of a multivariate geometric distribution (MGD) have been derived. A modification of the MLE estimator (modified MLE) has been derived in which case the bias is reduced. The mean square...
Research Article

A Comprehensive Study on Power of Tests for Normality

Hadi Alizadeh Noughabi
Pages: 647 - 660
Many statistical procedures assume that the underling distribution is normal. In this paper, we consider the popular and powerful tests for normality and investigate the power values of these tests to detect deviations from normality. The family of fourparameter generalized lambda distributions (FMKL)...
Research Article

Bayesian Premium Estimators for Mixture of Two Gamma Distributions Under Squared Error, Entropy and Linex Loss Functions: With Informative and Non Informative Priors

Fatma Zohra Attoui, Halim Zeghdoudi, Ahmed Saadoun
Pages: 661 - 673
In this paper, we consider the Zeghdoudi distribution as the conditional distribution of Xn | 𝜃, we focus on estimation of the Bayesian premium under three loss functions (squared error which is symmetric, Linex and entropy, which are asymmetric), using non-informative and informative priors (the extension...
Research Article

On Properties and Applications of a Two-Parameter Xgamma Distribution

Subhradev Sen, N. Chandra, Sudhansu S. Maiti
Pages: 674 - 685
An existing one-parameter probability distribution can be very well generalized by adding an extra parameter in it and, in turn, the two-parameter family of distributions, thus obtained, provides added flexibility in modeling real life data. In this article, we propose and study a two-parameter generalization...
Research Article

On the Lindley Record Values and Associated Inference

A. Fallah, A. Asgharzadeh, S.M.T.K. MirMostafaee
Pages: 686 - 702
In this paper, we discuss the record values arising from the Lindley distribution. We compute the means, variances and covariances of the record values. These values are used to compute the best linear unbiased estimators (BLUEs) and the best linear invariant estimators (BLIEs) of the location and scale...
Research Article

Weighted Entropy Measure: A New Measure of Information with ts Properties in Reliability Theory and Stochastic Orders

M. Mahdy
Pages: 703 - 718
The weighted entropy measure is a germane dynamic measure of uncertainty in reliability and survival studies. In this paper, the new results of weighted entropies with some characterizations are provided. Furthermore, we have presented some results for weighted entropy residual and weighted past residual...
Research Article

Weibull-Normal Distribution and its Applications

Felix Famoye, Eno Akarawak, Matthew Ekum
Pages: 719 - 727
In this paper, a Weibull-normal distribution, based on the standard quantile function of log-logistic distribution, is defined and studied. Some properties of the probability distribution are discussed. The Weibull-normal distribution is found to be unimodal or bimodal. The distribution can be right...