TITLE:
On Marginal Distributions under Progressive Type II Censoring: Similarity/Dissimilarity Properties
AUTHORS:
Amal Helu, Hani Samawi
KEYWORDS:
Weitzman’s Measure, Progressive Censoring, Marginal Density, Type II Censoring
JOURNAL NAME:
Open Journal of Statistics,
Vol.7 No.4,
August
11,
2017
ABSTRACT:
Currently, progressive censoring is intensively investigated by several researchers
due to its ability to remove subjects from the experiment before the
final termination point, thus saving time and cost. The closed form of marginal
density of failure times under progressive type II censoring is essential to
study the properties of statistical analysis under different censoring schemes.
In this paper, we provide a different presentation of the marginal distribution
under progressive type-II censoring and we derive closed forms for different
special cases. In order to study the similarity/dissimilarity of marginal densities
of order statistics for failure times, the overlap measure is used. We discovered
that the overlap measure depends only on the effective size m. A numerical
example based on a real life data regarding failure times of aircrafts'
windshields is provided to quantify the amount of redundant information
provided by the order statistics of the failure times under different progressive
type-II schemes based on the overlap measure. Moreover, this data set is used
as a pilot study to estimate the effective size m needed for future studies.