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Title: Generalized Rayleigh-exponential-Weibull distribution and progressively type-I interval-censored data Authors:  Din Chen - University of North Carolina (United States) [presenting]
Yuhlong Lio - University of South Dakota (United States)
Tanita Cronje - University of Pretoria (South Africa)
Abstract: A new family of 3-parameter Generalized Rayleigh-Exponential-Weibull(GREW) distributions is proposed to unify the family of 2-parameter Generalized Rayleigh (GR) distribution, the family of 2-parameter Generalized Exponential (GE) distribution and the family of 2-parameter Weibull (W) distribution. This GREW distribution includes a variety of commonly used statistical distributions, such as, Rayleigh distribution, GR distribution, exponential distribution, GE distribution, Weibull distribution, etc., and therefore can provide better model fitting in real applications. We illustrate the application of this new GREW distribution to fit a typical progressive type-1 interval-censored data from 112 patients with plasma cell myeloma treated at the National Cancer Institute and show the superior model fitting using the value of fitted log-likelihood function and the Kolmogorov-Smironov goodness-of-fit statistic. A series of Monte-Carlo simulation studies are further designed to evaluate the performance of parameter estimation for this new distribution family.