| Author | Fang, Tsu-shang Emma |
| Call Number | AIT Thesis no. CS-87-07 |
| Subject(s) | Distribution (Probability theory)
|
| Note | A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science, School of Engineering and Technology |
| Publisher | Asian Institute of Technology |
| Series Statement | Thesis ; no. CS-87-07 |
| Abstract | The 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. |
| Year | 1987 |
| Corresponding Series Added Entry | Asian Institute of Technology. Thesis ; no. CS-87-07 |
| Type | Thesis |
| School | School of Engineering and Technology |
| Department | Other Field of Studies (No Department) |
| Academic Program/FoS | Computer Science (CS) |
| Chairperson(s) | Huynh Ngoc Phien; |
| Examination Committee(s) | Venkatachalam, Paruvachi A. ;Aagesen, Finn Arve ; |
| Scholarship Donor(s) | R. 0. C. Government; |
| Degree | Thesis (M.Sc.) - Asian Institute of Technology, 1987 |