The McDonald Gumbel model

ABSTRACT

We propose a new model called the McDonald Gumbel distribution, the major advantage of which is its ability to fit asymmetric real data that can not be properly adjusted by existing distributions. This model contains as special models the Gumbel, exponentiated Gumbel (Persson and Rydén, 2010), beta Gumbel (Nadarajah and Kotz, 2004), Kumaraswamy Gumbel distributions, among others. We obtain the ordinary moments, quantile and generating functions and mean deviations. The method of maximum likelihood is used to fit the proposed distribution. The applicability of the new model is illustrated by means of two real data sets.

KEYWORDS:

• Gumbel distribution
• maximum likelihood
• McDonald distribution
• moment-generating function
• quantile function.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E10
• 62P99

Notes

1 http://functions.wolfram.com/06.23.06.0004.01 - Accessed 26/06/2013.