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.
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.