1 AIT Asian Institute of Technology

Statistical simulation : estimation methods for the general extreme value distribution

AuthorFang, Tsu-shang Emma
Call NumberAIT Thesis no. CS-87-07
Subject(s)Distribution (Probability theory)

NoteA thesis submitted in partial fulfillment of the requirements for the degree of Master of Science, School of Engineering and Technology
PublisherAsian Institute of Technology
Series StatementThesis ; no. CS-87-07
AbstractThe General (or generalized) Extreme Value (GEV) distribution is a versatile three- parameter family of distributions including the three types of extremal models, namely Gumbel (Type I), Frechet (Type II) and Weibull (Type III) distributions. The nature of observations whose behavior may be modelled using this generalized extreme - value distribution makes it quite likely that samples will be censored either on the left, the right or both ends. In this study, an attempt was made to derive all the formulas needed to compute the maximum likelihood estimators in any of the above situations ; related computer programs were subsequently developed to facilitate the use of theoretical formula s. Th e properties of the estimators whereby were investigated. Moreover, the variance-covariance matrix o f the maximum likelihood estimators was approximated by the inverse of the observed information matrix and the one of Fisher information matrix. All needed formulas for computing the Fisher information matrix were derived for both cases, complete and censored samples. Simulated results showed that in almost all cases, the maxi mum likelihood estimators were better than the probability weighted moment (PWM) estimators; However, the PWM estimator-s ha d less bias in uncensored case. Moreover, the variance-covariance matrix of the parameter estimators was better approximated by the inverse of the observe d information matrix . Finally, Akaike' s Information criterion was used for the choice of extremal models . . Simulated results showed that it is very sensitive to choose type II and type III extreme models from the GEV distribution.
Year1987
Corresponding Series Added EntryAsian Institute of Technology. Thesis ; no. CS-87-07
TypeThesis
SchoolSchool of Engineering and Technology
DepartmentOther Field of Studies (No Department)
Academic Program/FoSComputer Science (CS)
Chairperson(s)Huynh Ngoc Phien;
Examination Committee(s)Venkatachalam, Paruvachi A. ;Aagesen, Finn Arve ;
Scholarship Donor(s)R. 0. C. Government;
DegreeThesis (M.Sc.) - Asian Institute of Technology, 1987


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