Normal distribution with plasticizing component

Abstract

In this article, we introduce a new flexible plasticizing component and mixture of two distributions, further called the normal distribution with the plasticizing component. Some properties of the introduced distributions are derived, such as the cumulative distribution and the probability density function, moments, skewness and kurtosis. The unknown parameters are estimated by the maximum likelihood method. Illustrative examples of applicability and flexibility of the introduced distributions are given. We compare the flexibility of the introduced distribution and various distributions using skewness and kurtosis.

Keywords:

• Mixture of two normal distributions
• compound distribution
• departure from normality
• random number generator
• maximum likelihood estimator

Notations

The following notations will be used throughout the article:

Table

Acknowledgements

The author thanks the Editor, the Associate Editor, and the Referees for their useful suggestions and comments which have significantly improved the article.

Notes

1 In mathematical environments such as Mathcad, SciLab and R is $0^0=1.$