Adel Mohamed Mahmoud Omar
Prediction intervals for future ordered observations in doubly type-II censored samples from a two parameter exponential distribution. Part (1)
Preprint series: Mathematica Gottingensis
MSC:
62E17 Approximations to distributions (nonasymptotic)
Abstract: This project deals with the problem on prediction for future ordered observations in doubly type-II censored samples from a two parameter exponential distribution.
Let $X_{(1)}, X_{(2)},...,X_{(n)}$ be the corresponding order statistics. We assume that for some k and r with $1\leq k\leq r$k\leq i\leq r$are observed. On the basis of the observations$X_{(k)}, X_{(k+1)},...,X_{(r)}$we have to determine an interval which contains the value of$X_{(s)}$for some$r\leq s\leq n$with specified probability. we use a classical approach based on the statistic$T=\displaystyle{\sum_{i=k+1}^{r}X_{(i)}+(n-r)X_{(r)}-(n-k)X_{(k)}}$we determine a prediction interval for$X_{(s)}\$. We have derived maximum likelihood estimates based on doubly type-II censored samples , with these estimated parameter values
we determine a maximum likelihood predictor. We have studied the Bayesian approach when the prior distribution for the parameter is given by a two parameter gamma distribution.
Keywords: prediction intervals , censored samples , exponential distribution