Abstract
Providing a new distribution is always precious for statisticians. A new three-parameter distribution called the gamma normal distribution is defined and studied. Various structural properties of the new distribution are derived, including some explicit expressions for the moments, quantile and generating functions, mean deviations, probability weighted moments and two types of entropy. We also investigate the order statistics and their moments. Maximum likelihood techniques are used to fit the new model and to show its potentiality by means of two examples of real data. Based on three criteria, the proposed distribution provides a better fit then the skew-normal distribution.
Highlights
The statistical analysis of lifetime data plays an important role in medicine, epidemiology, biology, demography, economics, engineering and other fields
Our main aim of the study is to examine the role of the bivariate frailty model based on the reversed hazard rate in survival studies
For this we used the inverse Gaussian frailty with two baseline distribution and these models are compared with their baseline models based on reversed hazard rate
Summary
The statistical analysis of lifetime data plays an important role in medicine, epidemiology, biology, demography, economics, engineering and other fields. Clayton (1978) introduced the notion of shared relative-risk for the analysis of survival data. There are many striking similarities between the statistics derived from this distribution and those of the normal; see Chhikara and Folks (1986) These properties make it potentially attractive for modeling purposes with survival data. The reversed hazard rate is more useful in estimating reliability function when the data are left censored or right truncated. Andersen et al (1993), Lawless (2003) have discussed the use of reversed hazard rate for the analysis of left censored or right truncated data. Sankaran and Gleeja (2011) introduced frailty as a common random effect that acts multiplicatively on reversed hazard rates, which is useful for the analysis of left censored data. In the present paper we introduce three parametric shared frailty model with inverse Gaussian frailty using reversed hazard rate.
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