STUDIES ON GENERAL EXTREME VALUE DISTRIBUTION

Abstract

The probability plots ( graphical approach ) are used to fit the probability distribution to given series, to identify the outliers and to assess goodness of fit. The graphical approach requires probability of exceedence or non exceedence of various events. This is obtainedthrough the use of plotting position formula. In literature many plotting position formulae have been reported. All of the many existing formulae 'provide different results particularly at the tails of the distribution and hence there is need of unbiased plotting position formulae for different distributions. The General Extreme Value (GEV) distribution is commonly used for flood frequency analysis, and covers the Gumbel distribution as a special case which has been recommended by Central Water Commision (India). For G1V distribution the probability of non exceedence is related with expected value of reduced variates. In the study the expected value of reduced variates have been obtained using theoretically derived equations and using synthetically generated data for different values of shape parameters of GEV distribution. The theoretically derived equations use concept of probability weighted moments and order statistics.Different forms of unbiassed plotting position formulae have been developed using regression analysis for entire range of k and sample sizes. a (v) The developed plotting possition formulae along with other existing formulae have been compared with expected value of theoretically derived reduced variates on the basis of (i) over. all fit, (ii) fit in the upper tail region and (iii) fit in the lower tail region. On the basis of analysis carried out in the study the following formulae is recommended for use by field engineers. _ in - 0.02y - 0.32 I:m n .4+fir3 ~ for k~ 0 _ _ in - 0.29 for k = 0