A comparison of different procedures relating to parameter estimation in extreme value type 1 distribution through simulation

URI http://harp.lib.hiroshima-u.ac.jp/it-hiroshima/metadata/9779
File
Title
A comparison of different procedures relating to parameter estimation in extreme value type 1 distribution through simulation
Author
氏名 Pal Satyabrata
ヨミ
別名
氏名 Kageyama Sanpei
ヨミ カゲヤマ サンペイ
別名 景山 三平
氏名 Pal Subhabaha
ヨミ
別名
Subject
EV I(2) distribution
Moment estimator
MLE
Simulation
Normality
Abstract

The extreme value (EV) distribution is widely used for fitting and analyzing a long range of data emanated from different real-life situations. Annual maximum water-flow data collected from a river over a considerable period of time (say, about 30 years) are found to follow the EV distribution very satisfactorily. Also the distribution of annual maximum rainfall data in a region closely follows the EV distribution. Thus these distributions have important applications in the works related to the flood frequency estimation/estimation of return period flood. The estimation of parameters from these types of data (data following the EV type I with two parameters, EV I(2), distribution) has important use in the field of hydrology to understand the situation more deeply. Here an investigation is made through simulation for several pairs of values of a and b (parameters of the EV I(2) distribution) using different sample sizes in order to compare the accuracy of maximum likelihood method as well as method of moments in estimating the original parameters (the pairs of values of a and b for which the simulation is done). A module is developed in SAS/IML which deals with a random number generation in the EV I(2) distribution and the subsequent estimation of parameters with method of moments and maximum likelihood method. It is found that when the parameter value of a is less than or equal to 0.5, the method of moments produce more accurate estimators of the parameters than the corresponding maximum likelihood estimators for large samples (250 or more). An error distribution investigation with respect to the parameters is also made with CAPABILITY and QQPLOT procedures in SAS/QC. It is found that when the sample size is small (10, 100, etc.) the error distribution follows near normality but with the increase in sample sizes (200, 300, etc.) the error distribution gradually deviates much away from normality. Some procedures in SAS/BASE and SAS/STAT are used in the calculation leading to the final results.

Journal Title
広島工業大学紀要. 研究編
Volume
45
Spage
281
Epage
289
Published Date
2011
Publisher
広島工業大学
ISSN
1346-9975
NCID
AA11599110
NAID
40018724494
Language
eng
NIIType
Departmental Bulletin Paper
Text Version
出版社版
Old URI
Set
it-hiroshima