Abstract
The five parameter Kumaraswamy generalized gamma model (Pas coa et al., 2011) includes some important distributions as special cases and it is very useful for modeling lifetime data. We propose an extended version of this distribution by assuming that a shape parameter can take negative values. The new distribution can accommodate increasing, decreasing, bath tub and unimodal shaped hazard functions. A second advantage is that it also includes as special models reciprocal distributions such as the recipro cal gamma and reciprocal Weibull distributions. A third advantage is that it can represent the error distribution for the log-Kumaraswamy general ized gamma regression model. We provide a mathematical treatment of the new distribution including explicit expressions for moments, generating function, mean deviations and order statistics. We obtain the moments of the log-transformed distribution. The new regression model can be used more effectively in the analysis of survival data since it includes as sub models several widely-known regression models. The method of maximum likelihood and a Bayesian procedure are used for estimating the model pa rameters for censored data. Overall, the new regression model is very useful to the analysis of real data.
Highlights
Standard lifetime distributions usually present very strong restrictions to produce bathtub curves, and appear to be unappropriate for data with this characteristic
This result enables us to obtain the ordinary moments of the Kumaraswamy generalized gamma (KGG) order statistics as infinite weighted sums of convenient quantities defined by δs,r =
We introduce an extended form of the Kumaraswamy generalized gamma (KGG) distribution (Pascoa et al, 2011) for which the hazard rate function accommodates the four types of shape forms, i.e. increasing, decreasing, bathtub and unimodal
Summary
Standard lifetime distributions usually present very strong restrictions to produce bathtub curves, and appear to be unappropriate for data with this characteristic. Ortega et al (2009) proposed a modified GG regression model to allow the possibility that long-term survivors may be presented in the data and Cordeiro et al (2010) defined the exponentiated generalized gamma (EGG) distribution This distribution due to its flexibility in accommodating many forms of the risk function seems to be an important model that can be used in a variety of problems in survival analysis. The Kumaraswamy generalized gamma (KGG) distribution (Pascoa et al, 2011) can model four types of the failure rate function (i.e. increasing, decreasing, unimodal and bathtub) depending on the values of its parameters It is suitable for testing goodness-of-fit of some sub-models, such as the EGG, GG, EW, Weibull and GR distributions.
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