
ISO Abbrev. Title: Pol. J. Environ. Stud.DOI: 10.15244/pjoes/63782
Vol. 25, No. 6 (2016), 22552264

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

Ishfaq Ahmad^{1}, Muhammad Fawad^{1}, Muhammad Akbar^{1},
Aamar Abbas^{2}, Hafiz Zafar^{3}

^{1}Department of Mathematics and Stats, International Islamic University, Islamabad, Pakistan
^{2}Department of Mathematics, The University of Poonch, AJK, Rawalakot, Pakistan
^{3}Department 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., linearmoments (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). Lmoments ratio diagram and Ztest 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 Download full text: PDF

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