Analyzing survival data with highly negatively skewed distribution: The Gompertz-sinh family
In this article, we explore a new two-parameter family of distribution, which is derived by suitably replacing the exponential term in the Gompertz distribution with a hyperbolic sine term. The resulting new family of distribution is referred to as the Gompertz-sinh distribution, and
it possesses a thicker and longer lower tail than the Gompertz family, which is often used to model highly negatively skewed data. Moreover, we introduce a useful generalization of this model by adding a second shape parameter to accommodate a variety of density shapes as well as nondecreasing
hazard shapes. The flexibility and better fitness of the new family, as well as its generalization, is demonstrated by providing well-known examples that involve complete, group, and censored data.
Keywords: gompertz distribution; goodness-of-fit; maximum likelihood
Document Type: Research Article
Affiliations: 1: Department of Mathematics, Central Michigan University, Mount Pleasant, MI, USA 2: Department of Mathematical Sciences, University of Nevada, Las Vegas, NV, USA
Publication date: 01 January 2010
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