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.