On Generalized Inverse Pareto Family of Distributions: Properties and Applications

Music City Center 

This study proposes new families of generalized inverse Pareto distributions using the T-R{Y} framework. Several
choices for the distributions of the random variables T and Y lead to generalized families of the random variable R,
which, in this study, is characterized by the inverse Pareto distribution. The generalized family of distributions is
thus named as T-inverse Pareto{Y} family. We consider the exponential, Weibull, log-logistic, logistic, Cauchy, and
extreme value distribution as potential choices for the distribution of the random variable Y . Specific members of
the T-inverse Pareto{Y} family exhibit symmetric, skewed to the right, skewed to the left, unimodal, or bimodal
density functions. Some statistical properties of the T-inverse Pareto{Y} family are investigated. The method of
maximum likelihood is proposed for estimating the distribution parameters and its performance is assessed using
a simulation study. Four real-world datasets from different disciplines are analyzed to demonstrate the flexibility of the
proposed T-inverse Pareto{Y} family of distributions.

T-R{Y} framework

Inverse Pareto distribution

Quantile function

Maximum likelihood estimation

Censoring 

Section on Statistical Computing