1
1735-1294
Statistical Research and Training Center - Statistical Centre of Iran
214
General
Testing Skew-Laplace Distribution Using Density-based Empirical Likelihood Approach
Safavinejad
M.
Jomhoori
S.
Alizadeh Noughabi
H.
1
9
2016
13
1
1
24
23
11
2016
23
11
2016
Abstract: In this paper, we first describe the skew-Laplace distribution and its properties. We then introduce a goodness of fit test for this distribution according to the density-based empirical likelihood ratio concept. Asymptotic consistency of the proposed test is demonstrated.
The critical values and Type I error of the test are obtained by Monte Carlo simulations.
Moreover, the empirical distribution function (EDF) tests are considered for the skew-Laplace distribution to show they do not have acceptable Type I error in comparison with the proposed test. Results show that the proposed test has an excellent Type I error which does not depend on the unknown parameters.
The results obtained from simulation studies designed to investigate the power of the test are presented, too. The applicability of the proposed test in practice is demonstrated by real data examples.
215
General
Tsallis Entropy Properties of Order Statistics and Some Stochastic Comparisons
Baratpour
Simindokht
Khammar
Amirhamzeh
1
9
2016
13
1
25
41
23
11
2016
23
11
2016
Abstract: Tsallis entropy and order statistics are important in engineering reliability, image and signal processing. In this paper, we try to extend the concept of Tsallis entropy using order statistics. For this purpose, we propose the Tsallis entropy of order statistics and for it we obtain upper and lower bounds and some results on stochastic comparisons.
216
General
Preliminary Test and Shrinkage Estimations of Scale Parameters for Two Exponential Distributions based on Record Values
Zakerzadeh
Hojatollah
Jafari
Akbar
Karimi
Mahdieh
1
9
2016
13
1
43
58
23
11
2016
23
11
2016
Abstract: The exponential distribution is applied in a very wide variety of statistical procedures. Among the most prominent applications are those in the field of life testing and reliability theory. When there are two record samples available for estimating the scale parameter, a preliminary test is usually used to determine whether to pool the samples or use the individual sample. In this paper, the preliminary test estimator and shrinkage estimator are studied. The optimum level of significance for preliminary test estimation and the optimum values of shrinkage coefficient are obtained based on minimax regret criterion under the weighted square error loss function.
217
General
Admissible Set of Rival Models based on the Mixture of Kullback-Leibler Risks
Sayyareh
Abdolreza
1
9
2016
13
1
59
88
23
11
2016
23
11
2016
Abstract: Model selection aims to find the optimum model. A good model will generally yield good results. Herein lies the importance of model evaluation criteria for assessing the goodness of a subjective model. In this work we want to answer to this question that, how could infinite set of all possible models that could have given rise to data, be narrowed down to a reasonable set of statistical models? This paper considers a finite mixture of the known criterion to the model selection problem to answer to the question. The aim of this kind of criteria is to select an reasonable set of models based on a measure of closeness. We demonstrate that a very general class of statistical criterion, which we call that finite mixture Kullback-Leibler criterion, provides a way of rival theory model selection. In this work we have proposed two types of coefficients for the mixture criterion, one based on the density and another one based on the risk function. The simulation study and real data analysis confirme the proposed criteria.
218
General
Stress-strength Reliability of Exponential Distribution based on Type-I Progressively Hybrid Censored Samples
Mirjalili
M.
Torabi
H.
Nadeb
H.
Bafekri. F.
S.
1
9
2016
13
1
89
105
23
11
2016
23
11
2016
Abstract: This paper considers the estimation of the stress-strength parameter, say R, based on two independent Type-I progressively hybrid censored samples from exponential populations with different parameters. The maximum likelihood estimator and asymptotic confidence interval for R are obtained. Bayes estimator of R is also derived under the assumption of independent gamma priors. A Monte Carlo simulation study is used to evaluate the performance of maximum likelihood estimator, Bayes estimator and asymptotic confidence interval. Finally, a pair of real data sets is analyzed for illustrative purposes.
219
General
Bayesian Method for Finding True Change Point when a Control Chart is used
Dehghan Monfared
Esmail
Lak
Fazlollah
1
9
2016
13
1
107
117
23
11
2016
23
11
2016
Abstract: The process personnel always seek the opportunity to improve the processes. One of the essential steps for process improvement is to quickly find the starting time or the change point of a process disturbance. To do this, after a control chart triggers an out-of-control signal, an order of points in time (known as a plan) should be identified such that if the process examined sequentially at them, the true change point is detected as soon as possible. A typical method is to start the examination of the process from the signal time of the control chart and proceed to neighbouring points. In this paper, we establish a Bayesian method to solve this problem, i.e. to find a plan for examining the process sequentially such that it minimizes the Bayes risk among all other possible plans. At last, our proposed Bayes method is applied to a normal process, and compared to a typical method which is usually used to find the true change point through a series of simulations.