# ISO Abbrev. Title: Pol. J. Environ. Stud.

DOI: 10.15244/pjoes/63782

Vol. 25, No. 6 (2016), 2255-2264

# Regional Frequency Analysis of Annual Peak Flows in Pakistan Using Linear Combination of Order Statistics

1Department of Mathematics and Stats, International Islamic University, Islamabad, Pakistan
2Department of Mathematics, The University of Poonch, AJK, Rawalakot, Pakistan
3Department of Statistics, University of Sargodha Pakistan

Abstract: For this paper we conducted a regional analysis (RA) of annual peak flows using linear combination of order statistics, i.e., linear-moments (LM) and trimmed linear moments (TLM). Design flood estimates are calculated and compared at different return periods, which are useful for water resources management, including hydrological structures and basin management. The main objective of our study was to compare regional design flood estimates for untrimmed and trimmed samples. LM is the special case of TLM, when we have no trimming from either side. First, regional flood frequency analysis is performed for LM and then for TLM. After initial screening of the annual peak flow series, a discordancy measure was used to diagnose the discordant sites. No site was found to be discordant. For homogeneity of the region, the homogeneity measure “H” was employed using simulation study based on Kappa distribution, and found that the nine sites on the Indus Basin included in the study constitute a single homogeneous region. In this study we used TLM with trimming values (γ, 0), where γ = 1, 2, 3, 4. In order to determine the most appropriate probability distribution for regional quantile estimates, different probability distributions are used, namely: generalized extreme value (GEV), generalized pareto (GPA), generalized logistic (GLO), Pearson type three (PE3), and generalized normal (GNO). L-moments ratio diagram and Z-test as goodness of fit are engaged to identify the most suitable probability distribution. A comparison revealed that GNO is the best distribution for first three cases as (0, 0), (1, 0), and (2, 0), while for the last two cases of (3, 0) and (4, 0) the most appropriate choice is GEV. A simulation study was also carried out to evaluate the performance and robustness of the best fit probability distribution using relative bias (RB) and relative root mean square error (RRMSE).

## Keywords: regional quantiles, linear moments, simulation, Kappa distribution, relative bias

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