Lomax-Rayleigh distribution: traditional and heuristic methods of estimation

Abstract

Abstract We introduce a continuous distribution called the Lomax-Rayleigh (L-R) distribution that extends the Lomax distribution. The generalization of the probability density function, cumulative distribution function of this distribution and the expression for moment generating function was established. We considered a traditional methods of estimation such as the maximum likelihood method and nonlinear least square estimation method to estimate the parameters and utilizing the Artificial Intelligence Algorithms such as Genetics Algorithm and pattern search method in estimation process. A comparison study among that methods is carried out through simulation experiments. We concluded that pattern search method is more efficient than other methods depending upon mean square error criteria.