The Properties of Bivariate Geometric Distribution-Type II

Author(s):  
Xu Xiaoling ◽  
Gu Beiqing ◽  
Wang Ronghua
2019 ◽  
Vol 36 (4) ◽  
pp. 569-586
Author(s):  
Ricardo Puziol Oliveira ◽  
Jorge Alberto Achcar

Purpose The purpose of this paper is to provide a new method to estimate the reliability of series system by using a discrete bivariate distribution. This problem is of great interest in industrial and engineering applications. Design/methodology/approach The authors considered the Basu–Dhar bivariate geometric distribution and a Bayesian approach with application to a simulated data set and an engineering data set. Findings From the obtained results of this study, the authors observe that the discrete Basu–Dhar bivariate probability distribution could be a good alternative in the analysis of series system structures with accurate inference results for the reliability of the system under a Bayesian approach. Originality/value System reliability studies usually assume independent lifetimes for the components (series, parallel or complex system structures) in the estimation of the reliability of the system. This assumption in general is not reasonable in many engineering applications, since it is possible that the presence of some dependence structure between the lifetimes of the components could affect the evaluation of the reliability of the system.


2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
J. B. Shah ◽  
M. N. Patel

We derive Bayes estimators of reliability and the parameters of a two- parameter geometric distribution under the general entropy loss, minimum expected loss and linex loss, functions for a noninformative as well as beta prior from multiply Type II censored data. We have studied the robustness of the estimators using simulation and we observed that the Bayes estimators of reliability and the parameters of a two-parameter geometric distribution under all the above loss functions appear to be robust with respect to the correct choice of the hyperparameters a(b) and a wrong choice of the prior parameters b(a) of the beta prior.


Author(s):  
Aisha Fayomi ◽  
Hamdah Al-Shammari

This paper deals with the problem of parameters estimation of the Exponential-Geometric (EG) distribution based on progressive type-II censored data. It turns out that the maximum likelihood estimators for the distribution parameters have no closed forms, therefore the EM algorithm are alternatively used. The asymptotic variance of the MLEs of the targeted parameters under progressive type-II censoring is computed along with the asymptotic confidence intervals. Finally, a simple numerical example is given to illustrate the obtained results.


2015 ◽  
Vol 05 (07) ◽  
pp. 721-729 ◽  
Author(s):  
Azhari A. Elhag ◽  
Omar I. O. Ibrahim ◽  
Mohamed A. El-Sayed ◽  
Gamal A. Abd-Elmougod

1996 ◽  
Vol 46 (1-2) ◽  
pp. 23-28 ◽  
Author(s):  
G. Asha ◽  
N. Unnikrishnan Nair

In this paper two characterizations in terms of the properties of the residuai life distribution of a bivariate seometric model is established.


2018 ◽  
Vol 20 (1) ◽  
pp. 320-326 ◽  
Author(s):  
MOHAMMAD BASYUNI ◽  
HIROSHI SAGAMI ◽  
SHIGEYUKI BABA ◽  
HIROSUKE OKU

Basyuni M, Sagami H, Baba S, Oku H. 2019. Response of polyisoprenoid concentration and profile in three groups of mangrove seedlings of coping with long-term salinity. Biodiversitas 20: 320-326. The response of polyisoprenoid (polyprenol and dolichol) concentration and distribution was investigated with three groups mechanism of coping with salinity: a secreting mangrove species of Avicennia officinalis, a non-secreting species (excluder) of Bruguiera cylindrica, and a salt-accumulating species of Xylocarpus granatum. The seedlings of three mangroves were grown under 0 and 3% salinity concentration for five months. Polyisoprenoids in the lipid extracts were examined by two-dimensional thin layer chromatography (2D-TLC). The pattern of the polyprenols and dolichols in the leaves and roots were categorized as two types (I and II). In category I, dolichols dominated over polyprenols, however, in category II, the existence of both polyprenols and dolichols was found. In the leaves, type-I was observed in A. officinalis under 0 and 3% salinity. On the other hand, type-II was found in B. cylindrica and X. granatum under 0 and 3% salt concentrations. A similar pattern was found in the roots, A. officinalis (type-I), and that in B. cylindrica and X. granatum was type-II. This finding depicted that the seedlings of A. officinalis, B. cylindrica, and X. granatum leaves and roots imply no change in the distribution type: the categories were distributed as type I or II under 0% salt concentrations, as well as type-I or II under 3% salt concentrations. This study implied that polyisoprenoids may play a protective function against salinity in the mangrove leaves and roots of three groups scheme (secreting, excluding, and accumulating) of salt management.


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