1
1726-4057
Iranian Statistical Society
344
On the reliability of complex systems with three dependent components per element
Razmkhah
Mostafa
^{
b
}
Saberzade
Zahra
^{
b
}Department of Statistics, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran.
1
6
2017
16
1
1
17
22
02
2016
22
02
2016
The complex system containing n elements, each having three dependent components, is described. The reliability function of such systems is investigated using a trivariate binomial model. In addition, the mean residual life function of a complex system with intact components at time t is derived. The results are simplified for a trivariate Farlie-Gumbel-Morgenstern family with standard exponential marginal distribution functions. The effect of various parameters on the reliability and mean residual life functions are studied via some graphical representations.
347
62Cxx: Decision theory
Admissibility in a One Parameter Non-regular Family with Squared-log Error Loss Function
Moradi Zahraie
Shirin
Zakerzadeh
Hojatollah
1
6
2017
16
1
19
31
20
03
2016
30
01
2017
Consider an estimation problem in a one-parameter non-regular distribution when both endpoints of the support depend on a single parameter. In this paper, we give sufficient conditions for a generalized Bayes estimator of a parametric function to be admissible. Some examples are given.
362
60Exx: Distribution theory
On the Finite Mixture Modelling via Normal Mean-variance Birnbaum-Saunders Distribution
Naderi
Mehrdad
Arabpour
Alireza
Jamalizadeh
Ahad
1
6
2017
16
1
33
51
10
07
2016
20
02
2017
This paper presents a new finite mixture model using the normal mean-variance mixture of Birnbaum-Saunders distribution. The proposed model is multimodal with wider ranges of skewness and kurtosis. Moreover, it is useful for modeling highly asymmetric data in various theoretical and applied statistical problems. The maximum likelihood estimates of the parameters of the model are computed iteratively by feasible EM algorithm. To illustrate the finite sample properties and performance of the estimators, we conduct a simulation study and illustrate the usefulness of the new model by analyzing a real dataset.
318
62Fxx: Parametric inference
Inferences for Extended Generalized Exponential Distribution based on Order Statistics
Abbasnejad
Maliheh
1
6
2017
16
1
53
67
11
10
2015
28
11
2016
Recently, a new distribution, named as extended generalized exponential distribution, has been introduced by Kundu and Gupta (2011). In this paper, we consider the extended generalized exponential distribution with known shape parameters α and β. At first, the exact expressions for marginal and product moments of order statistics are derived. Then, these values are used to obtain the necessary coefficients for the best linear unbiased estimators and L-moments estimators of the location and scale parameters. The mean squared errors of these estimators are also given and compared.
351
Characterizations of Certain Marshall-Olkin Generalized Distributions
Hamedani
Gholamhossein
1
6
2017
16
1
69
75
25
04
2016
25
04
2016
Several characterizations of Marshall-Olkin generalized distributions, introduced by Gui (2013) and by Al-Saiari et al. (2014) are presented. These characterizations are based on: (i) a simple relationship between two truncated moments ; (ii) the hazard function.
381
62Jxx: Linear inference, regression
On the Bayesian Sequential Change-Point Detection
Gholami
Gholamhossein
^{
k
}
^{
k
}Department of Mathematics, Faculty of Sciences, Urmia University, Iran
1
6
2017
16
1
77
94
15
09
2016
15
09
2016
The problems of sequential change-point have several important applications in quality control, signal processing, and failure detection in industry and finance and signal detection. We discuss a Bayesian approach in the context of statistical process control: at an unknown time τ, the process behavior changes and the distribution of the data changes from p0 to p1. Two cases are considered: (i) p0 and p1 are fully known, (ii) p0 and p1 belong to the same family of distributions with some unknown parameters θ1≠θ2. We present a maximum a posteriori estimate of the change-point which, for the case (i), can be computed in a sequential manner. In addition, we propose the use of the Shiryaev's loss function. Under this assumption, we define a Bayesian stopping rule. For the Poisson distribution and in the two cases (i) and (ii), we obtain results for the conjugate prior.