Bayesian Prediction of Order Statistics Based on k-Record Values from a Generalized Exponential Distribution

Zoran Vidović

doi:10.3390/stats2040031

Abstract

We examine in this paper the implementation of Bayesian point predictors of order statistics from a future sample based on the k th lower record values from a generalized exponential distribution.

Highlights

Let { Xn, n ≥ 1} be a sequence of independent and identically distributed random variables with a cumulative distribution function F ( x; θ ) and a probability density function f ( x; θ ), where θ ∈ Θ could be a real-valued vector
The motivation behind this research follows from the point predictors of order statistics of a future sample from an exponential distribution based on the upper kth record values published in
We addressed the problem of presenting Bayesian point predictors of order statistics of a future sample of size m based on the kth lower record values from a generalized exponential distribution (GED)

Summary

Introduction

Let { Xn , n ≥ 1} be a sequence of independent and identically distributed (iid) random variables with a cumulative distribution function (cdf) F ( x; θ ) and a probability density function (pdf) f ( x; θ ), where θ ∈ Θ could be a real-valued vector. The definition of the kth record values is as follows: For a fixed k, we define the sequence { Tn,k , n ≥ 1}, of the kth lower record times of { Xn , n ≥ 1} as follows: T1,k = 1, Tn+1,k = min{ j > Tn,k : Xk:Tn,k +k−1 > Xk:j+k−1 }, n ≥ 1, where X j:n denotes the jth order statistic of the sample The problem of predicting record values and order statistics from two independent sequences following two parameter exponential distributions was extensively discussed in [8]. The motivation behind this research follows from the point predictors of order statistics of a future sample from an exponential distribution based on the upper kth record values published in [9]. We deal with point predictors of order statistics based on the lower kth record values from the generalized exponential distribution.

Prior Information and Predictive Distributions

Prediction Intervals of Order Statistics

Point Predictors of Order Statistics

An Illustrative Examples

Conclusions

Methods