A new class of skew distributions with climate data analysis

Abstract

In this paper, we develop a new general class of skew distributions with flexibility properties on the tails. Moreover, such class can provide heavy and light tails. Some of its mathematical properties are studied, including the quantile function, the moments, the moment generating function and the mean of deviations. New skew distributions are derived and used to construct new models capturing asymmetry inherent to data. The estimation of the class parameters is investigated by the method of maximum likelihood and the performance of the estimators is assessed by a simulation study. Applications of the proposed distribution are explored for two climate data sets. The first data set concerns the annual heat wave index and the second data set involves temperature and precipitation measures from the meteorological station located at Schiphol, Netherlands. Data fitting results show that our models perform better than the competitors.

Keywords:

• Asymmetry
• skewed distribution
• stochastic representation
• heat wave index
• regression

2000 MSC:

• 60E05
• 62E15

Acknowledgments

The authors thank the two anonymous reviewers and Associate Editor for their careful reading of the paper and a number of valuable comments, which have contributed to significantly improve the presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).