Let the regression model be Y i = β 1 X i + ε i , where ε i are i. i. d. N (0, σ 2 ) random errors with variance σ 2 > 0 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 slope, regression parameter β 2 . The problem of study is when and where this change has started occurring. This is called change point inference problem. The estimators of m, β 1 , β 2 are derived under asymmetric loss functions, namely, Linex loss & General Entropy loss functions. The effects of correct and wrong prior information on the Bayes estimates are studied.
A sequence of independent lifetimes X 1 , . . . , X m , X m+1 , . . . , X n was observed from Maxwell distribution with reliability r 1 (t) at time t 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 reliability r 2 (t) at time t. The Bayes estimators of m, θ 1 , θ 2 are derived under different asymmetric loss functions. The effects of correct and wrong prior information on the Bayes estimates are studied.
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