Bayes Estimation of Shift Point in Geometric Sequence

Abstract

A sequence of independent lifetimes X 1 X 2 X m , X m+1 X n were observed from geometric population with parameter q 1 but later it was found that there was a change in the system at some point of time m and it is reflected in the sequence after X m by change in parameter q 2 . The Bayes estimates of m q 1 q 2 , reliability R 1 t and R 2 t at time t are derived for symmetric and asymmetric loss functions under informative and non informative priors. A simulation study is carried out.

Bayesian Estimation of Reliability Function for A Changing Exponential Family Model under Different Loss Functions

“…where θ 1 , θ 2 > 0 and m=1, …, (n -1) The joint posterior density of θ 1 , θ 2 and m is obtained by using equations (12), (18) for poissonmodel, and (13), (19)…”

“…(2002), Wu and Tiau (2005) and Zhang and Wu (2005) considered the applications ofCUSUM control charts. Bayes estimation of unknown shift point in geometric distribution is studied by Shah and Patel (2006); Many of statisticians like Chin and Broemeling (1980), Calabria and Pulcini (1994), Zacks (1983), Pandaya and Jani (2006), Shah andPatel (2007, 2009), Chib (2998), Altessimo and Corradi (2003) and Fiteni (2004) studied the shift point Models in Bayesian framework, and Bayesian estimation of shift point in poisson Model is studied by gorakhpour university's authors (2012).…”

Bayes Estimation of Shift Point in Normal Sequence and Its Application to Statistical Process Control

“…A variety of shift point problems have been studied in Bayesian Shift Point Estimation in Normal Sequence 561 framework by many authors like Zack (1983), Calabria and Pulcini (1994), Pandya and Jani (2006), and Shah and Patel (2007). Chin Choy and Broemeling (1980), Chib (1998), Altissimo and Corradi (2003), and Fiteni (2004) studied applications of change point models in econometrics.…”

A Bayesian detection of structural changes in autoregressive time series models

“…From a Bayesian point of view, the problem of detecting a change has received much attention and has been studied by many authors like Cherno and Zacks (1964), Kander and Zacks (1966), Sen and Srivastava (1975), Jani and Pandya (1999), Fan and Chen (2005) and Shah and Patel (2007). Ming Ng (1990) analyzed a linear model in which both the mean and the precision change once at an unknown time point, the posterior distributions of the change point, and the ratio of the precisions are derived.…”