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Papers by Fadi Shaayo
Journal of Al-Nahrain University Science
In this thesis, we consider the extreme value distn. of two parameters for the reason of its appe... more 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 distribution. such as moments and higher moments are collected and unified and the properties of reliability and hazard functions of the distribution are illustrated.
The chi-square goodness - of - fit is used to test whether the generated samples from the standardized extreme value distribution by Monte Carlo simulation are acceptable for use.
These samples are used to estimate the distribution 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".
In this paper, right censored data of type II related to the Gumbel distribution (maximum extreme... more In this paper, right censored data of type II related to the Gumbel distribution (maximum extreme value distribution) of two parameters is considered. Estimation of the distribution parameters are presented by two methods: maximum likelihood method and modified moment method. Moments properties of the estimators such as bias, variance, skewness and kurtosis are compared between two methods. We show that the estimators are unbiased, and its variances converge to zero, which the estimators are consistent in modified moment method. Consistency of the maximum likelihood and modified moment estimators are tabulated by using mean square error. Confidence interval estimation for the distribution parameters based on the maximum likelihood method and modified moment method are given by Monte Carlo simulation.
Journal of Al-Nahrain University Science
In this thesis, we consider the extreme value distn. of two parameters for the reason of its appe... more 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 distribution. such as moments and higher moments are collected and unified and the properties of reliability and hazard functions of the distribution are illustrated.
The chi-square goodness - of - fit is used to test whether the generated samples from the standardized extreme value distribution by Monte Carlo simulation are acceptable for use.
These samples are used to estimate the distribution 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".
In this paper, right censored data of type II related to the Gumbel distribution (maximum extreme... more In this paper, right censored data of type II related to the Gumbel distribution (maximum extreme value distribution) of two parameters is considered. Estimation of the distribution parameters are presented by two methods: maximum likelihood method and modified moment method. Moments properties of the estimators such as bias, variance, skewness and kurtosis are compared between two methods. We show that the estimators are unbiased, and its variances converge to zero, which the estimators are consistent in modified moment method. Consistency of the maximum likelihood and modified moment estimators are tabulated by using mean square error. Confidence interval estimation for the distribution parameters based on the maximum likelihood method and modified moment method are given by Monte Carlo simulation.