Some Contributions to Description and Validation of the Extreme Value Distribution
(2009) Abstract
 This thesis focuses on the validation and description of the Gumbel distribution. Since this is a scale and location parameter distribution, the generalized least squares regression of the order statistics on the expected values can be used, without the necessity of iteration, to obtain the best linear unbiased estimates of the parameters.
In order to implement this procedure, we need information about the expected values and variancescovariances of order statistics from the standard extreme value distribution. Numerical problems in determining these values and lack of exact values of means, variances for n > 100 and covariances for n > 30, are major challenges which we must deal with.
In two... (More)  This thesis focuses on the validation and description of the Gumbel distribution. Since this is a scale and location parameter distribution, the generalized least squares regression of the order statistics on the expected values can be used, without the necessity of iteration, to obtain the best linear unbiased estimates of the parameters.
In order to implement this procedure, we need information about the expected values and variancescovariances of order statistics from the standard extreme value distribution. Numerical problems in determining these values and lack of exact values of means, variances for n > 100 and covariances for n > 30, are major challenges which we must deal with.
In two papers, by applying the method of least squares, we present approximation algorithms to approximate the means, variances and covariances of the order statistics of the standard extreme value distribution. In both papers we compare the accuracy of our proposed models by using available tabulated values and values obtained from Monte Carlo methods.
In the case where one or both of the parameters in the distribution are known or unknown, as in papers three to six, we present and compare goodnessoffit tests based on different approaches. These papers tackle tests of the null hypothesis that a random sample comes from the extreme value distribution of type I (minima). The test procedure is to calculate an appropriate test statistic and reject null hypothesis if the value of the statistic used exceeds the percentage point at the type I error level. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1389276
 author
 PirouziFard, MirNabi ^{LU}
 supervisor

 Björn Holmquist ^{LU}
 opponent

 Professor Shukur, Ghazi, Jönköping International Business School
 organization
 publishing date
 2009
 type
 Thesis
 publication status
 published
 subject
 keywords
 weighted least squares estimator., probability plot, power of tests, extreme value distribution, variances and covariances, goodnessoffit tests, order statistics, Approximations of means
 pages
 128 pages
 defense location
 EC3:207, Holger Crafoords Ekonomicentrum
 defense date
 20090515 14:00:00
 ISBN
 9789162877910
 language
 English
 LU publication?
 yes
 id
 a9b05bc0736f46a1ba38872017194167 (old id 1389276)
 date added to LUP
 20160404 13:41:46
 date last changed
 20181121 21:15:40
@phdthesis{a9b05bc0736f46a1ba38872017194167, abstract = {This thesis focuses on the validation and description of the Gumbel distribution. Since this is a scale and location parameter distribution, the generalized least squares regression of the order statistics on the expected values can be used, without the necessity of iteration, to obtain the best linear unbiased estimates of the parameters. <br/><br> <br/><br> In order to implement this procedure, we need information about the expected values and variancescovariances of order statistics from the standard extreme value distribution. Numerical problems in determining these values and lack of exact values of means, variances for n > 100 and covariances for n > 30, are major challenges which we must deal with.<br/><br> <br/><br> In two papers, by applying the method of least squares, we present approximation algorithms to approximate the means, variances and covariances of the order statistics of the standard extreme value distribution. In both papers we compare the accuracy of our proposed models by using available tabulated values and values obtained from Monte Carlo methods. <br/><br> <br/><br> In the case where one or both of the parameters in the distribution are known or unknown, as in papers three to six, we present and compare goodnessoffit tests based on different approaches. These papers tackle tests of the null hypothesis that a random sample comes from the extreme value distribution of type I (minima). The test procedure is to calculate an appropriate test statistic and reject null hypothesis if the value of the statistic used exceeds the percentage point at the type I error level.}, author = {PirouziFard, MirNabi}, isbn = {9789162877910}, language = {eng}, school = {Lund University}, title = {Some Contributions to Description and Validation of the Extreme Value Distribution}, year = {2009}, }