Confidence bands for exponential distribution functions under progressive type-II censoring

TL;DR

This paper develops confidence bands for the exponential distribution function under progressive type-II censoring, providing explicit formulas and comparing their performance through analysis and data examples.

Contribution

It introduces a new method for constructing confidence bands using confidence regions and Kolmogorov-Smirnov statistics, including a novel confidence region for location-scale parameters.

Findings

Explicit formulas for confidence band boundaries and coverage probabilities.

Comparison of band width and area demonstrating performance.

Extension discussions to related models and distributions.

Abstract

Based on a progressively type-II censored sample from the exponential distribution with unknown location and scale parameter, confidence bands are proposed for the underlying distribution function by using confidence regions for the parameters and Kolmogorov-Smirnov type statistics. Simple explicit representations for the boundaries and for the coverage probabilities of the confidence bands are analytically derived, and the performance of the bands is compared in terms of band width and area by means of a data example. As a by-product, a novel confidence region for the location-scale parameter is obtained. Extensions of the results to related models for ordered data, such as sequential order statistics, as well as to other underlying location-scale families of distributions are discussed.