American Society of Civil Engineers

Log Pearson Type 3 Distribution: Method of Mixed Moments

by Donthamsetti Veerabhadra Rao, M.ASCE, (Hydro., St. Johns River Water Management District, Palatka, Fla.)

Journal of the Hydraulics Division
, Vol. 106, No. 6, June 1980, pp. 999-1019

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Document type: Journal Paper
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Abstract: Two new methods of moments (MO) which do not use the sample skewness coefficient (CS) are evolved for fitting log Pearson type 3 distribution (LP). The two current MO methods which use CS are: (Method 1) real data are fit to LP; or (Method 2) logarithmic data are fit to P (Pearson type 3 distribution). By virtue of the combined properties of P and LP, it is shown that: (Method 3) skewness coefficient (γ) of LP can be estimated from the mean of logarithmic data (Y¯); or (Method 4) skewness of coefficient of P (γ) can be estimated from the mean of real data (X¯). The values (Y¯) and (X¯) are unbiased estimates while CS is generally a biased estimate. Monto Carlo experiments have indicated that, as sample size becomes small, the estimates for quantiles of LP are: (1) Systematically biased for Method 1; (2) highly positive biased when (γ) is negative, and unbiased to somewhat positively biased when (γ) is positive for Method 2; (3) unbiased to least biased of the four methods when (γ) is negative, and somewhat negatively biased when (γ) is positive for Method 3; and (4) negatively biased for Method 4.

ASCE Subject Headings:
Flood frequency
Frequency distribution
Probability distribution
Low flow
Probability density functions