The probability distributions of Gumbel, 3‐parameter log‐normal (LN3), general extreme values (GEV), 3‐parameter gamma (G3), and 3‐parameter log‐gamma (LG3), whose parameters are computed by the methods of moments (MOM), maximum‐likelihood (ML), probability‐weighted moments (PWM), and self‐determined probability‐weighted moments (SDPWM) are compared from the aspect of predicting the right‐tail quantiles of return periods in the range: 10 ≤ T ≤ 10,000 years from finite‐length sample series by a Monte Carlo analysis. The parameters of the LN3 distribution are also computed by the method of ‘zero‐sample‐skewness’. Synthetic series of 1Million elements having skewness coefficients: +0.5, +1, +2, +3, +5 are generated by LN3, GEV, and G3 distributions, separately, resulting in 15 different 1Million‐element synthetic series (= 5 skewnesses × 3 distributions). The right‐tail quantiles having exceedence probabilities (Pex): 0.1, 0.05, 0.02, 0.01, 0.005, 0.002, 0.001, 0.0005, 0.0002, 0.0001 are first computed by the parent distribution. The right‐tail quantiles having those Pex's are also computed by these 21 probability models using all 1Million/n short series of lengths: n = 20, 30, 50, 100, 200. Instead of biases and root‐mean‐square‐errors of 1Million/n differences of quantiles from those of the parent distribution separately for individual return periods (T), like 100 years, 1000 years, etc., which has been the usual procedure so far, mean relative differences (MRDj's), mean absolute relative differences (MARDj's), standard deviations of relative differences (SDRDj's), and standard deviations of absolute relative differences (SDARDj's) of the areas between the frequency curves of the short series and the frequency curve of the parent distribution over the entire range: 0.0001 ≤ Pex ≤ 0.1 are proposed. Ranked tables of MRDj's, MARDj's, SDRDj's, and SDRDj's computed from 1Million/n n‐element series are investigated as a more comprehensive criterion of goodness of a probability distribution to predict right‐tail population quantiles from short‐length sample series. The G3‐PWM distribution is found to be better, followed by the LN3‐MOM, LN3‐PWM, G3‐MOM, GEV‐MOM, and LN3‐ML distributions for the ranges covered.