Toward the establishment of a family of distributions that may fit any dataset

ABSTRACT

This article presents a review and comparison of the most important expanded families of distributions. We set the essential requirements by which an expanding family can fit any dataset successfully. A new method is proposed to construct families, which fulfill these essential requirements. Consequently, two families are suggested, which are more tractable than many other known families and possess very wide range of the indices of skewness and kurtosis. The article is motivated by two applications to real dataset.

KEYWORDS:

• Data modeling
• Full family of distributions
• Kurtosis
• Mixture distribution
• Skewness

MATHEMATICS SUBJECT CLASSIFICATION:

• 62-07
• 62E10
• 62F99

Acknowledgments

The authors are grateful to the Editor in Chief, Professor N. Balakrishnan, and the referees for suggestions and comments that improved the presentation substantially.