Detailed abstract of the manuscript:
Hosking, J.R.M., J.R. Wallis, and E.F. Wood. (1985). Estimation of the
Generalized Extreme-Value Distribution by the Method of Probability-Weighted
Moments. Technometrics 27(3), 251–261.
Extended methods and derivations are available in
Probability distributions and parameter estimation: HoskingEtAl1985.
Open the vignette locally with
vignette("distributions-and-estimation", package = "EnvStats").
Forbes, C., M. Evans, N. Hastings, and B. Peacock. (2011). Statistical Distributions. Fourth Edition. John Wiley and Sons, Hoboken, NJ.
Greenwood, J.A., J.M. Landwehr, N.C. Matalas, and J.R. Wallis. (1979). Probability Weighted Moments: Definition and Relation to Parameters of Several Distributions Expressible in Inverse Form. Water Resources Research 15(5), 1049–1054.
Hoeffding, W. (1948). A Class of Statistics with Asymptotically Normal Distribution. Annals of Mathematical Statistics 19, 293–325.
Hosking, J.R.M. (1985). Algorithm AS 215: Maximum-Likelihood Estimation of the Parameters of the Generalized Extreme-Value Distribution. Applied Statistics 34(3), 301–310.
Hosking, J.R.M. (1990). \(L\)-Moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics. Journal of the Royal Statistical Society, Series B 52(1), 105–124.
Hosking, J.R.M., and J.R. Wallis (1995). A Comparison of Unbiased and Plotting-Position Estimators of \(L\) Moments. Water Resources Research 31(8), 2019–2025.
Jenkinson, A.F. (1969). Statistics of Extremes. Technical Note 98, World Meteorological Office, Geneva.
Johnson, N. L., S. Kotz, and A.W. Kemp. (1992). Univariate Discrete Distributions. Second Edition. John Wiley and Sons, New York, pp.4-8.
Johnson, N. L., S. Kotz, and N. Balakrishnan. (1995). Continuous Univariate Distributions, Volume 2. Second Edition. John Wiley and Sons, New York.
Lehmann, E.L. (1975). Nonparametrics: Statistical Methods Based on Ranks. Holden-Day, Oakland, CA, 457pp.