The Beta Exponentiated Gumbel Distribution

We introduce a new five-parameter distribution called the beta exponentiated Gumbel (BEG) distribution that includes the beta Gumbel, exponentiated Gumbel and Gumbel distribution. Expressions for the distribution function, density function and rth moment of the new distribution and order statistics are obtained. We discuss estimation of the parameters by maximum liklelihood and provide the information matrix. Using a real data set, we observe that the BEG distribution is flexible and can be used quite eectively in analysing positive data in place of the special cases. Keywords. Beta Gumbel distribution, Exponentiated Gumbel, Gumbel distribution, Information matrix, Maximum likelihood estimation.