Testing for Membership to the IFRA and the NBU Classes of Distributions

Radhendushka Srivastava, Ping Li, Debasis Sengupta
Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, PMLR 22:1099-1107, 2012.

Abstract

This paper provides test procedures to determine whether the probability distribution underlying a set of non-negative valued samples belongs to the Increasing Failure Rate Average (IFRA) class or the New Better than Used (NBU) class. Membership of a distribution to one of these classes is known to have implications which are important in reliability, queuing theory, game theory and other disciplines. Our proposed test is based on the Kolmogorov-Smirnov distance between an empirical cumulative hazard function and its best approximation from the class of distributions constituting the null hypothesis. It turns out that the least favorable distribution, which produces the largest probability of Type I error of each of the tests, is the exponential distribution. This fact is used to produce an appropriate cut-off or p-value. Monte Carlo simulations are conducted to check small sample size (i.e., significance) and power of the test. Usefulness of the test is illustrated through the analysis of a set of monthly family expenditure data collected by the National Sample Survey Organization of the Government of India.

Cite this Paper

BibTeX
@InProceedings{pmlr-v22-srivastava12, title = {Testing for Membership to the IFRA and the NBU Classes of Distributions}, author = {Srivastava, Radhendushka and Li, Ping and Sengupta, Debasis}, booktitle = {Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics}, pages = {1099--1107}, year = {2012}, editor = {Lawrence, Neil D. and Girolami, Mark}, volume = {22}, series = {Proceedings of Machine Learning Research}, address = {La Palma, Canary Islands}, month = {21--23 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v22/srivastava12/srivastava12.pdf}, url = {https://proceedings.mlr.press/v22/srivastava12.html}, abstract = {This paper provides test procedures to determine whether the probability distribution underlying a set of non-negative valued samples belongs to the Increasing Failure Rate Average (IFRA) class or the New Better than Used (NBU) class. Membership of a distribution to one of these classes is known to have implications which are important in reliability, queuing theory, game theory and other disciplines. Our proposed test is based on the Kolmogorov-Smirnov distance between an empirical cumulative hazard function and its best approximation from the class of distributions constituting the null hypothesis. It turns out that the least favorable distribution, which produces the largest probability of Type I error of each of the tests, is the exponential distribution. This fact is used to produce an appropriate cut-off or p-value. Monte Carlo simulations are conducted to check small sample size (i.e., significance) and power of the test. Usefulness of the test is illustrated through the analysis of a set of monthly family expenditure data collected by the National Sample Survey Organization of the Government of India.} }
Endnote
%0 Conference Paper %T Testing for Membership to the IFRA and the NBU Classes of Distributions %A Radhendushka Srivastava %A Ping Li %A Debasis Sengupta %B Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2012 %E Neil D. Lawrence %E Mark Girolami %F pmlr-v22-srivastava12 %I PMLR %P 1099--1107 %U https://proceedings.mlr.press/v22/srivastava12.html %V 22 %X This paper provides test procedures to determine whether the probability distribution underlying a set of non-negative valued samples belongs to the Increasing Failure Rate Average (IFRA) class or the New Better than Used (NBU) class. Membership of a distribution to one of these classes is known to have implications which are important in reliability, queuing theory, game theory and other disciplines. Our proposed test is based on the Kolmogorov-Smirnov distance between an empirical cumulative hazard function and its best approximation from the class of distributions constituting the null hypothesis. It turns out that the least favorable distribution, which produces the largest probability of Type I error of each of the tests, is the exponential distribution. This fact is used to produce an appropriate cut-off or p-value. Monte Carlo simulations are conducted to check small sample size (i.e., significance) and power of the test. Usefulness of the test is illustrated through the analysis of a set of monthly family expenditure data collected by the National Sample Survey Organization of the Government of India.
RIS
TY - CPAPER TI - Testing for Membership to the IFRA and the NBU Classes of Distributions AU - Radhendushka Srivastava AU - Ping Li AU - Debasis Sengupta BT - Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics DA - 2012/03/21 ED - Neil D. Lawrence ED - Mark Girolami ID - pmlr-v22-srivastava12 PB - PMLR DP - Proceedings of Machine Learning Research VL - 22 SP - 1099 EP - 1107 L1 - http://proceedings.mlr.press/v22/srivastava12/srivastava12.pdf UR - https://proceedings.mlr.press/v22/srivastava12.html AB - This paper provides test procedures to determine whether the probability distribution underlying a set of non-negative valued samples belongs to the Increasing Failure Rate Average (IFRA) class or the New Better than Used (NBU) class. Membership of a distribution to one of these classes is known to have implications which are important in reliability, queuing theory, game theory and other disciplines. Our proposed test is based on the Kolmogorov-Smirnov distance between an empirical cumulative hazard function and its best approximation from the class of distributions constituting the null hypothesis. It turns out that the least favorable distribution, which produces the largest probability of Type I error of each of the tests, is the exponential distribution. This fact is used to produce an appropriate cut-off or p-value. Monte Carlo simulations are conducted to check small sample size (i.e., significance) and power of the test. Usefulness of the test is illustrated through the analysis of a set of monthly family expenditure data collected by the National Sample Survey Organization of the Government of India. ER -
APA
Srivastava, R., Li, P. & Sengupta, D.. (2012). Testing for Membership to the IFRA and the NBU Classes of Distributions. Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 22:1099-1107 Available from https://proceedings.mlr.press/v22/srivastava12.html.

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