On diagnostic devices for proposing half-logistic and inverse half-logistic models using generalized (k) record values

ABSTRACT

In this work we consider the generalized upper (k) record values (GURV’s) and generalized lower (k) record values (GLRV’s) arising from half-logistic distribution (HLD) and inverse half-logistic distribution (IHLD). We derive some characterization results of HLD based on some moment relations of generalized upper (k) record values and those of generalized lower (k) record values and accordingly devised some diagnostic tools to identify HLD as a model to the distribution of a population. Similar characterization theorems and diagnostic tools are developed for IHLD as well. Simulation studies are conducted to validate the diagnostic tools devised for both HLD and IHLD.

Keywords:

• Characterizations
• Diagnostic methods
• Generalized upper (k) record values
• Generalized lower (k) record values
• Half-logistic distribution
• Inverse half-logistic distribution
• Recurrence relations

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G30
• 62E10
• 60E05

Acknowledgments

The authors are highly grateful to the reviewers for many of their constructive comments which lead to remarkable improvement on the revised version of the paper.

Additional information

Funding

The first author expresses his gratefulness to Kerala State Council for Science, Technology & Environment for supporting him financially in the form of Emeritus Scientist Award (Order No. 0.01/KESS/2015/KSCSTE dtd 17-12-2015).