An alternative method for proposing new families of distributions: Estimation of parameters through classical and Bayesian analysis

Abstract

In this article, a novel method named as an alternative family of distributions for proposing new continuous probability distributions is suggested. The novelty of the proposed scheme is highlighted by considering Log-Logistic distribution as a special case. Important properties of the AL family of distributions are derived. The inferential section of the AL family, primarily, includes the maximum likelihood estimation. The diversity of parameter estimation is encountered for complete and censoring phenomena along with Bayesian Paradigm. The ironic property of the maximum likelihood estimates of the unknown parameters of the proposed family of distributions is assessed by rigorous simulation study for complete and censored phenomena.  Further, three real data sets have been used to illustrate the applicability of the new scheme.