Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
15
2
2019
3
1
Model Selection for Mixture Models Using Perfect Sample
173
212
EN
Sadegh
Fallahigilan
Razi University
sadegh.falahi@yahoo.com
Abdolreza
Sayyareh
K. N. Toosi University of Technology
asayyareh@kntu.ac.ir
10.29252/jsri.15.2.173
We have considered a perfect sample method for model selection of finite mixture models with either known (fixed) or unknown number of components which can be applied in the most general setting with assumptions on the relation between the rival models and the true distribution. It is, both, one or neither to be well-specified or mis-specified, they may be nested or non-nested. We consider mixture distribution as a complete-data (bivariate) distribution by prediction of missing data variable (unobserved variable) and show that this ideas is applicable to use Vuongchr('39')s test for select optimum mixture model when number of components are known (fixed) or unknown. We have considered AIC and BIC based on the complete-data distribution. The performance of this method is evaluated by Monte-Carlo method and real data set, as Total Energy Production.
finite mixture model, perfect sample, model selection, missing data variable, Vuong's test.
http://jsri.srtc.ac.ir/article-1-308-en.html
http://jsri.srtc.ac.ir/article-1-308-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
15
2
2019
3
1
Bayesian Sample Size Determination for Joint Modeling of Longitudinal Measurements and Survival Data
213
236
EN
Taban
Baghfalaki
Tarbiat Modares University
t.baghfalaki@modares.ac.ir
10.29252/jsri.15.2.213
A longitudinal study refers to collection of a response variable and possibly some explanatory variables at multiple follow-up times. In many clinical studies with longitudinal measurements, the response variable, for each patient is collected as long as an event of interest, which considered as clinical end point, occurs. Joint modeling of continuous longitudinal measurements and survival time is an approach for accounting association between two outcomes which frequently discussed in the literature, but design aspects of these models have been rarely considered.
This paper uses a simulation-based method to determine the sample size from a Bayesian perspective. For this purpose, several Bayesian criteria for sample size determination are used, of which the most important one is the Bayesian power criterion (BPC), where the determined sample sizes are given based on BPC. We determine the sample size based on treatment effect on both outcomes (longitudinal measurements and survival time). The sample size determination is performed
based on multiple hypotheses. Using several examples, the proposed Bayesian methods are illustrated and discussed. All the implementations are performed using R2OpenBUGS package and R 3.5.1 software.
Bayesian analysis, bayesian power criterion, longitudinal data, sample size determination, survival data, shared parameter model.
http://jsri.srtc.ac.ir/article-1-309-en.html
http://jsri.srtc.ac.ir/article-1-309-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
15
2
2019
3
1
Assessment and Estimation of the Coefficients of a Linear Model for Interval Data
237
274
EN
Amir Massoud
Malekfar
Allameh Tabataba'i University
malekfar1364@gmail.com
Farzad
Eskandari
Allameh Tabataba'i University
askandari@atu.ac.ir
10.29252/jsri.15.2.237
Imprecise measurement tools produce imprecise data. Interval,-valued (interval) data is one type of data which is usually used to deal with such imprecision. So, interval-valued variables have been used in the last decade. The relationships between the variables have recently been modeled by linear regression models. If interval response variables have any statistical distributions, the relationships are modeled in the linear models framework. In this paper, we propose new estimators for the parameters of an interval linear model under some conditions. Under the conditions, we demonstrate the theoretical adequacy of the estimators. Simulation studies and a real-life case study show the empirical adequacy and the practical applicability of the new estimators, respectively, under the conditions.
Interval-valued data, interval linear model, the theoretical and empirical adequacy of the estimators
http://jsri.srtc.ac.ir/article-1-310-en.html
http://jsri.srtc.ac.ir/article-1-310-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
15
2
2019
3
1
On Properties of a Class of Bivariate FGM Type Distributions
275
300
EN
Zahra
Sharifonnasabi
University of Isfahan
zahrash2013@gmail.com
Mohammad Hosein
Alamatsaz
University of Isfahan
alamatho@sci.ui.ac.ir
Iraj
Kazemi
University of Isfahan
ikazemi@stat.ui.ac.ir
10.29252/jsri.15.2.300
In this paper, we consider a new class of bivariate copulas and study their measures of association. Specifically, we propose a bivariate copula based distribution and obtain explicit expressions for the corresponding marginal and joint distributions of concomitants of generalized order statistics. Using these results, we provide the minimum variance linear unbiased estimator for the location and scale parameters of the concomitants of order statistics of Burr and logistic distributions. Then, we introduce a class of absolutely continuous bivariate distributions whose univariate margins are exponential distributions. In addition, we discuss their properties such as moment generating function, stress-strength probability and reliability of two component systems. Monte Carlo simulations are performed to highlight properties of the parameters estimates. Finally, we analyze two data sets to illustrate the flexibility and potential of the proposed distribution compared to several competing models.
Burr distribution, concomitants, exponential distribution, generalized order statistics, minimum variance, Monte Carlo simulation, reversed hazard rate.
http://jsri.srtc.ac.ir/article-1-311-en.html
http://jsri.srtc.ac.ir/article-1-311-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
15
2
2019
3
1
Shrinkage and Bayesian Shrinkage Estimation of the Expected Length of a M/M/1 Queue System
301
316
EN
Azadeh
Kiapour
Babol branch, Islamic Azad University
Kiapour@baboliau.ac.ir
Mehran
Naghizadeh Qomi
University of Mazandaran
m.naghizadeh@umz.ac.ir
10.29252/jsri.15.2.301
In this paper, shrinkage and Bayesian shrinkage
estimation of the expected length (l) in a M/M/1 queue system
is considered. A shrinkage estimator of l is considered when a
priori about l as l_0 is available. The bias and the risk of
shrinkage estimators are derived under a scale-invariant squared
error loss (SISEL) function. A class of Bayes shrinkage estimators
for $l$ is proposed which is a generalization of Bayes shrinkage
estimator and a relative performance of proposed estimators and the
maximum likelihood estimator (MLE) is performed. A simulated data is
given to illustrate the proposed results. Finally, we conclude with
a summary of our contributions.
Bayes shrinkage estimator, expected length, M/M/1 queue, scale-invariant squared error loss function.
http://jsri.srtc.ac.ir/article-1-312-en.html
http://jsri.srtc.ac.ir/article-1-312-en.pdf
Statistical Research and Training Center - Statistical Centre of Iran
Journal of Statistical Research of Iran JSRI
1735-1294
15
2
2019
3
1
A Quantile Approach to the Interval Shannon Entropy
317
333
EN
Mohammad
Khorashadizadeh
University of Birjand
m.khorashadizadeh@birjand.ac.ir
10.29252/jsri.15.2.317
In this paper, we introduce and study quantile version of the Shannon entropy function via doubly truncated (interval) lifetime, which includes the residual and past lifetimes as special case. We aim to study the use of proposed measure in characterization of distribution functions. Further, we describe a stochastic order and a weighted distribution based on this entropy and show their properties. Finally, some results have been obtained for some distributions such as Uniform, Exponential, Pareto I, Power function and Govindarajulu. Also by analysing a real data the subject has been illustrated.
Shannon entropy, quantile function, generalized failure rate, quantile doubly truncated Shannon entropy.
http://jsri.srtc.ac.ir/article-1-313-en.html
http://jsri.srtc.ac.ir/article-1-313-en.pdf