Closeness of k-records to Progressive Type-II Censored Order Statistics for Location-scale Families

Abstract

In this article, the Pitman closeness of upper and lower k-records to progressive Type-II censored order statistics for location-scale families is investigated. In each case, the special properties of the probability of Pitman closeness are obtained and the corresponding monotonicity properties are discussed. Moreover, the closest k-record to a specific progressive Type-II censored data is obtained. Finally, for the standard exponential and standard uniform distributions, explicit expressions for the probability of Pitman closeness are derived. For various censoring schemes, the results of the numerical computations are displayed in tables. Most of the results in Ahmadi and Balakrishnan (2013) can be achieved as special cases.

Keywords:

• Exponential distribution
• Record values
• Progressive Type-II censoring
• Pitman measure of closeness.

Mathematics Subject Classification:

• Primary 62G30
• Secondary 62G05.