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