On Modeling Heavy Tailed Medical Care Insurance data via a New Member of T-X family

Abstract

Heavy tailed distributions are worthwhile in modeling heavy tailed data. The researchers are often in search of such
distributions to provide best fit to heavy tailed data. In this article, a new T-X family member called, a new exponential
cosine-X family is introduced. A special sub-model of the proposed family, called, a new exponential cosine Weibull
distribution is studied in detail. Some mathematical properties along with the useful series expansion of distribution
and density functions of the proposed class are obtained. Two useful characterizations of this family are also provided.
We consider the maximum likelihood and Bayesian estimation procedures to estimate the parameters of the proposed
family. Monti Carlo simulation study is done to access the behavior of these estimators. For the illustrative purposes,
a real-life application of the proposed family to a heavy tailed medical care insurance data set is provided. Finally,
Bayesian analysis and performance of Gibbs sampling for the medical care are also carried out.