Developing Test Statistics to Identify Over- or Under-Dispersion in Parametric Lifetime Models

• Activity Number: 77
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
• Sponsor: Biometrics Section
• Author(s): Md. Rajibul Mian*+ and Sudhir Paul
• Companies: University of Windsor and University of Windsor
• Keywords: Score test ; Lifetime model ; Exponential family

Abstract

The one parameter exponential distribution is useful for modeling lifetime data. This distribution belongs to the exponential family of distributions and is a special case of a richer family of distributions, like the Pareto, the gamma and the Weibull distribution, all of which is two parameter distributions and can be expressed as a family of over-dispersed exponential models. The purpose of this research is to develop tests of goodness of fit of the exponential model against the over/under dispersed family of distributions. We have developed three score tests statistics S1, S2 and S3 for detecting over or under dispersion in lifetime data. S1 has been developed to detect general over/under dispersion and the other two statistics have been developed to detect specific over/under dispersion as represented by two extra-dispersed two parameter models. Further, a modification of S1 namely, MS1 has also been developed. From the simulation, we find that all the four statistics S1, MS1, S2 and S3 shows power properties reasonably well and they are capable to detect over/under dispersion of one kind or another. We extend these statistics for the type 1 and type 2 censored data.