The Transmuted Generalized Gamma Distribution: Properties and Application

Abstract

The unknown or unobservable risk factors in the survival analysis cause heterogeneity between individuals. Frailty models are used in the survival analysis to account for the unobserved heterogeneity in individual risks to disease and death. To analyze the bivariate data on related survival times, the shared frailty models were suggested. The most common shared frailty model is a model in which frailty act multiplicatively on the hazard function. In this paper, we introduce the shared inverse Gaussian frailty model with the reversed hazard rate and the generalized inverted exponential distribution and the generalized exponential distribution as baseline distributions. We introduce the Bayesian estimation procedure using Markov Chain Monte Carlo(MCMC) technique to estimate the parameters involved in the models. We present a simulation study to compare the true values of the parameters with the estimated values. Also we apply the proposed models to the Australian twin data set and a better model is suggested.

A geometric process with Hjorth marginal: Estimation, discrimination, and reliability data modeling

“…Let 𝑋 1 , … , 𝑋 𝑛 be random sample from Hjorth GP. In this case, we have Ŷ𝑖 observations by considering Equation (17). Also, we assume that the Ŷ(1) , Ŷ(2) , … Ŷ(𝑛) is the ordered sample of Ŷ𝑖 s. Thus, the MLS estimator of the 𝜃 and 𝜆 parameters can be obtained by minimizing the following utility function…”

“…As another set of practical data that could be modeled by the Hjort distribution, it can be pointed to the Reactor data set, which exemplifies the times between successive failures of a reactor's pumps in thousands of hours. Until today, the data set has been modeled using different models and has been reported to have a bathtub‐shaped hazard rate function (cf 15–17 …”

“…Until today, the data set has been modeled using different models and has been reported to have a bathtub-shaped hazard rate function (cf. [15][16][17] ). Furthermore, in Korkmaz et al, 18 the Reactor data set is modeled by using a Hjorth extension called Hjorth-Weibull, and it is reported that the extended model has optimal modeling performance.…”