A Study of Efficient Estimation Methods for the parameters of Extreme Value Distribution by Utilizing Monte Carlo Sampling

In this thesis, we consider the extreme value distn. of two parameters for the reason of its appearance in many statistical fields of applications. Mathematical and statistical properties of the distn. such as moments and higher moments are collected and unified and the properties of reliability and hazard functions of the distn. are illustrated. The chi-square goodness - of - fit is used to test whether the generated samples from the standardized extreme value distn. by Monte Carlo simulation are acceptable for use. These samples are used to estimate the distn. parameters by four methods of estimation, namely moments method, maximum likelihood method, order statistic method and least squares method. These methods are discussed theoretically and
assessed practically in estimating the reliability and hazard functions. The properties of the estimator, reliability and hazard functions, such as bias, variance, skewness, kurtosis, and mean square error are tabled. The computer programs are listed in three appendices and the run is made by using "MathCAD 14".