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A new method for adding two parameters to a family of distributions with application to the normal and exponential families

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Abstract

In this paper we introduce a new method to add two parameters to a family of distributions. Through the additional parameters we can fully control the skewness and kurtosis of the resulting family. This method is applied to yield a new two-parameter extension of the standard normal distribution, which may be positively–negatively asymmetric and leptokurtic–platykurtic. In addition, this method is applied to yield a new three-parameter extension of the exponential distribution, which may be symmetric and has non-constant hazard rate function.

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Acknowledgments

The author is grateful for the comments and suggestions by the referees and the Associated Editor. Their comments and suggestions have greatly improved the paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt

    H. M. Barakat

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  1. H. M. Barakat
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Correspondence to H. M. Barakat.

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Barakat, H.M. A new method for adding two parameters to a family of distributions with application to the normal and exponential families. Stat Methods Appl 24, 359–372 (2015). https://doi.org/10.1007/s10260-014-0265-8

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  • DOI: https://doi.org/10.1007/s10260-014-0265-8

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