A new generalized inverse Gaussian distribution with Bayesian estimators

A new family of distributions, called the transformed inverse Gaussian (TIG) distribution with four parameters, is introduced. Within this family, a specific distribution called the new generalized inverse Gaussian (NGIG) distribution, with three parameters, is examined in depth. Two distinct parameterizations for the NGIG distribution are presented, and the advantages, both computational and theoretical, of one parameterization over the other are discussed. The paper delves into maximum likelihood estimation techniques and compares them with Bayesian methods using Jeffreys-type priors for parameter estimation. It also establishes the propriety of the posterior distribution given certain conditions with this prior. The practical applicability of this distribution is demonstrated using real-world data.