Log-gamma-generated families of distributions. (English) Zbl 1326.62025
Summary: We introduce two new general families of continuous distributions, generated by a distribution \(F\) and two positive real parameters \(\alpha\) and \(\beta\) 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.
MSC:
| 62E15 | Exact distribution theory in statistics |
| 62E10 | Characterization and structure theory of statistical distributions |
| 60E05 | Probability distributions: general theory |
| 62F10 | Point estimation |
| 62G30 | Order statistics; empirical distribution functions |
| 62G32 | Statistics of extreme values; tail inference |
| 62P20 | Applications of statistics to economics |
Keywords:
gamma distribution; log-gamma distribution; order statistics; record statistics; skewness; heavy-tailed distributionReferences:
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