TR-36 : Comparative study of different parameter estimation techniques for EV-1 distribution

Abstract

Design of water resources structures needs estimation of hydrologic and meteorologic events for different return periods. This can be obtained through frequency analysis approach. The extreme value type 1 (EV-1) distribution is widely used for frequency analysis of extreme events in hydrology and meteorology. It's successful application depends upon the accuracy with which its parameters can be estimated. However, there is no universal agreed method of estimating its parameters.

This report explains and statistically compares various parameter estimation techniques cited in literature using data of different sample sizes generated by Monte Carlo simulation. These include (i) method of moments (MOM),(ii) Method of maximum likelihood (MLE), (iii) Method of probability weighted moments (PWM), (iv) Method based on principle of maximum entropy (POME), (v) Method of mixed moments (MIX), (vi) Method of least squares (LEAS) and (vii) In complete means procedure (ICM). All the above methods have been compared on the basis of (i) bias in location parameter (ii) bias in scale parameter, (iii) standard deviation of location parameter, (iv) standard deviation of scale Parameter, (v) efficiency in estimating location parameter, (vi) efficiency in estimating scale parameter, (vii) bias in quantile estimates, (viii) standard deviation of quantile estimates, (ix) efficiency of quantile estimates, (x) average of relative deviations between computed and expected value of reduced variates (DA) and (xi) average of squares of relative deviations between computed and expected value of reduced variates.

Based on criteria (i) to (ix) it is difficult to arrive at any definite conclusion as no method is the best according to all the criteria. However MIX and ICM are the least accurate methods. PWM, POME and MLE give nearly similar results and can be recommended for use. Based on criteria (x) and (xi) the ranks of different methods in descending orderare as follows:

Rank 1 2 3 4 5 6 7

Method PWM LEAS MLE POME MOM ICM MIX