Abstract:
Modeling extreme value theories is really gaining interest in the world with scientist working to improve the
flexibility of the distributions by adding parameter(s). Extreme value distributions are always described to include families of
Gumbel, Weibull and Frechet distributions. Of the three distributions, Gumbel distribution is the most commonly used in the
extreme value theory analysis. Existing literature has shown that the addition of parameter to a distribution makes it robust
and/or more flexible hence the study intends to improve the existing two parameters Gumbel distribution using the Marshall and
Olkin proposed method for introducing a new estimator/parameter to an existing distribution. The developed distribution will be
important to the applications in some life time studies like high temperature, earthquakes, network designs, horse racing, queues
in supermarket, insurance, winds, risk management, ozone concentration, flood, engineering and financial concepts. The
parameters for the introduced distribution was estimated using Maximum Likelihood Estimation method. The introduced three
parameters Gumbel distribution is a probability distribution function which can be used in modelling statistical data. The
maximum likelihood estimates for the three parameters namely shape, location and dispersion are efficient, sufficient and
consistent and this makes the function more flexible and better for application. The three parameters Gumbel distribution can be
used in modeling and analysis of normal data, skewed data and extreme data since it will provide efficient, sufficient and
consistent estimates.
