This function returns a list of the L-skew and L-kurtosis (\(\tau_3\) and \(\tau_4\), respectively) ordinates for construction of L-moment Ratio (L-moment diagrams) that are useful in selecting a distribution to model the data.
lmrdia()An R
list is returned.
The theoretical limits of \(\tau_3\) and \(\tau_4\); below \(\tau_4\) of the theoretical limits are theoretically not possible.
\(\tau_3\) and \(\tau_4\) lower limits of the Asymmetric Exponential Power distribution.
\(\tau^{(1)}_3\) and \(\tau^{(1)}_4\) of the Cauchy distribution (TL-moment [trim=1]).
\(\tau_3\) and \(\tau_4\) of the Exponential distribution.
\(\tau_3\) and \(\tau_4\) of the Generalized Extreme Value distribution.
\(\tau_3\) and \(\tau_4\) of the Generalized Logistic distribution.
\(\tau_3\) and \(\tau_4\) of the Generalized Pareto distribution.
\(\tau_3\) and \(\tau_4\) of the Gumbel distribution.
\(\tau_3\) and \(\tau_4\) of the Generalized Normal distribution.
\(\tau_3\) and \(\tau_4\) of the Govindarajulu distribution.
\(\tau_3\) and \(\tau_4\) of the Rayleigh distribution.
\(\tau_3\) and \(\tau_4\) of the Generalized Normal (3-parameter Log-Normal) distribution.
\(\tau_3\) and \(\tau_4\) of the Normal distribution.
\(\tau_3\) and \(\tau_4\) of the Pearson Type III distribution.
\(\tau_3\) and \(\tau_4\) of the Polynomial Density-Quantile3 distribution.
\(\tau_3\) and \(\tau_4\) of the reversed Govindarajulu.
\(\tau_3\) and \(\tau_4\) of the reversed Generalized Pareto.
\(\tau^{(1)}_3\) and \(\tau^{(1)}_4\) of the Slash distribution (TL-moment [trim=1]).
\(\tau_3\) and \(\tau_4\) of the uniform distribution.
\(\tau_3\) and \(\tau_4\) of the Weibull distribution (reversed Generalized Extreme Value).
W.H. Asquith
Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: Createspace Independent Publishing Platform, ISBN 978--146350841--8.
Asquith, W.H., 2014, Parameter estimation for the 4-parameter asymmetric exponential power distribution by the method of L-moments using R: Computational Statistics and Data Analysis, v. 71, pp. 955--970.
Hosking, J.R.M., 1986, The theory of probability weighted moments: Research Report RC12210, IBM Research Division, Yorkton Heights, N.Y.
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, v. 52, pp. 105--124.
Hosking, J.R.M., 1996, FORTRAN routines for use with the method of L-moments: Version 3, IBM Research Report RC20525, T.J. Watson Research Center, Yorktown Heights, New York.
Hosking, J.R.M., 2007, Distributions with maximum entropy subject to constraints on their L-moments or expected order statistics: Journal of Statistical Planning and Inference, v. 137, no. 9, pp. 2,870--2,891, tools:::Rd_expr_doi("10.1016/j.jspi.2006.10.010").
Hosking, J.R.M., and Wallis, J.R., 1997, Regional frequency analysis---An approach based on L-moments: Cambridge University Press.
plotlmrdia