Log Pearson Type 3 Distribution: Method of Mixed Moments

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.