In this paper, we present some methods for estimating the parameters of the two parameter Power function distribution. We use the least squares method (L.S.M), relative least squares method (R.L.S.M) and ridge regression method (R.R.M). Sampling behavior of the estimates is indicated by a monte carlo simulation. We use total deviation (T.D) and mean square error (M.S.E) to identify the best estimator among them. We determine the best method of estimation using different values for the parameters and different sample size.

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Estimation of magnitude and frequency of extreme rainfall has immense importance to make decisions about hydraulic structures like spillways, dikes and dams etc. This research involves the estimation of regional rainfall quantiles of 23 sites using L-moment based index flood regional frequency analysis. Initially, different tests are applied to check the assumptions of independence, stationarity and identical distribution. An L-moment based discordancy measure is used to detect discordant sites. Since in Pakistan, highly elevated area receive more rainfall. On the basis of this characteristic, the study region is divided into three regions which satisfy the L-moment based heterogeneity statistics using Monte Carlo simulations from Kappa distribution. The regional quantile estimates are obtained from GEV, GNO and GLO distributions which are found to be best choices for all three regions based on L-moment ratio diagram, Z-Statistics and average weighted difference values. For robust regional estimates, some accuracy measures are calculated using a simulation study of regional L-moment algorithm. On the basis of relative bias, relative absolute bias and relative RMSE, GNO is found be best robust for regional quantile estimation at lager return periods of 50, 100, 500 and 1000 and GEV at return periods of 1, 2, 5, 10 and 20 for all three regions.

This paper is concerned with the modifications of maximum likelihood, moments and percentile estimators of the two parameter Power function distribution. Sampling behavior of the estimators is indicated by Monte Carlo simulation. For some combinations of parameter values, some of the modified estimators appear better than the traditional maximum likelihood, moments and percentile estimators with respect to bias, mean square error and total deviation.

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