Log-gamma-generated families of distributions

Abstract

We introduce two new general families of continuous distributions, generated by a distribution F and two positive real parameters α and β which control the skewness and tail weight of the distribution. The construction is motivated by the distribution of k-record statistics and can be derived by applying the inverse probability integral transformation to the log-gamma distribution. The introduced families are suitable for modelling the data with a significantly skewed and heavy-tailed distribution. Various properties of the introduced families are studied and a number of estimations and data fitness on real data are given to illustrate the results.

Keywords:

• gamma distribution
• log-gamma distribution
• order statistics
• record statistics
• skewness
• heavy-tailed distribution

AMS Subject Classifications::

• 60E05
• 62E10
• 62F99

Acknowledgement

The authors thank the associate editor and anonymous referees for careful review of the manuscript and their comments and suggestions which improved the quality of the paper.