Confidence Bands for Exponential Distribution Functions under Progressive Type-II Censoring

Journal article

Stefan Bedbur, Fabian Mies
Journal of Statistical Computation and Simulation, vol. 92, 2022, pp. 60-80

DOI: 10.1080/00949655.2021.1931211

arXiv

Cite

APA Click to copy
Bedbur, S., & Mies, F. (2022). Confidence Bands for Exponential Distribution Functions under Progressive Type-II Censoring. Journal of Statistical Computation and Simulation, 92, 60–80. https://doi.org/10.1080/00949655.2021.1931211

Chicago/Turabian Click to copy
Bedbur, Stefan, and Fabian Mies. “Confidence Bands for Exponential Distribution Functions under Progressive Type-II Censoring.” Journal of Statistical Computation and Simulation 92 (2022): 60–80.

MLA Click to copy
Bedbur, Stefan, and Fabian Mies. “Confidence Bands for Exponential Distribution Functions under Progressive Type-II Censoring.” Journal of Statistical Computation and Simulation, vol. 92, 2022, pp. 60–80, doi:10.1080/00949655.2021.1931211.

BibTeX Click to copy

@article{bedbur2022a,
  title = {Confidence Bands for Exponential Distribution Functions under Progressive Type-II Censoring},
  year = {2022},
  journal = {Journal of Statistical Computation and Simulation},
  pages = {60-80},
  volume = {92},
  doi = {10.1080/00949655.2021.1931211},
  author = {Bedbur, Stefan and Mies, Fabian}
}

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.

Keywords: confidence set; coverage probability; finite sample inference; location-scale family; order statistics; simultaneous confidence intervals