Bayesian approach to prediction and the spacings in the exponential distribution

Abstract

SummaryA series of independent samples are drawn from a general population with positive variation f(x, ~), x>0. Based on the Bayesian approach, a general predictive distribution is given, to predict a statistic in the future sample based on the statistics in the earlier samples (or stages). Few general classes of distributions of this type like KoopmanPitman family, power function family and Burr's class of distributions are considered to show how this procedure works in predicting order statistics in the future sample. Also, the sum of the spacings in the future samples from an exponential population is predicted in terms of similar sum of spacings in the earlier samples. Discussion on the variance of this predictive distribution is dealt with. Finally, an illustrative example with simulated samples from an exponential population gives actual prediction of an order statistic as well as the sum of spacings in the future sample.

Class of Exponentiated Distributions Introduction

“…Lingappaiah (1979) suggested an extension to a series of M + 1 independent samples. The aim is to predict a statistic in a future sample based on earlier samples (or stages).…”

A study of shifting models in life tests via bayesian approach using semi-or-used priors (SOUPS)

“…Consider the samples 0, 1, 2, 3 from Lingappaiah [9] where r Below are two more simulated samples, samples 4 and 5 from the same population of Lingappaiah [9]. In (13), one can observe that if b>l, exponent of n~ negative which makes the large value of Q~-I manageable, though Q~-I continues to increase as k increases.…”

“…This prediction of order statistics in a future sample has been extensively analysed by many authors. For example, Dunsmore [1] and Lingappaiah [9]- [11] deal with this problem from the Bayesian point of view while Faulkenberry [2], Kaminsky [4], Lawless [5] and Lingappaiah [6], [7] treat this problem in the classical sense. In all these works a single sample or a series of samples are considered, all from the same model.…”

Bayesian Inference for the Left Truncated Exponential Distribution Based on Pooled Type-II Censored Samples

“…As in the case of estimation, a predictor can be either a point or an interval. Bayesian prediction for future observations from the exponential distribution has been discussed by many authors, including [11], [12], [13], [14], [15], [16], [17], [18], and [19].…”