lmrdia: L-moment Ratio Diagram Components

In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

L-moment Ratio Diagram Components

Description

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.

Usage

lmrdia()

Value

An R list is returned.

limits	The theoretical limits of \tau_3 and \tau_4; below \tau_4 of the theoretical limits are theoretically not possible.
aep4	\tau_3 and \tau_4 lower limits of the Asymmetric Exponential Power distribution.
cau	\tau^{(1)}_3 = 0 and \tau^{(1)}_4 = 0.34280842 of the Cauchy distribution (TL-moment [trim=1]) (see Examples lmomcau for source).
exp	\tau_3 and \tau_4 of the Exponential distribution.
gev	\tau_3 and \tau_4 of the Generalized Extreme Value distribution.
glo	\tau_3 and \tau_4 of the Generalized Logistic distribution.
gpa	\tau_3 and \tau_4 of the Generalized Pareto distribution.
gum	\tau_3 and \tau_4 of the Gumbel distribution.
gno	\tau_3 and \tau_4 of the Generalized Normal distribution.
gov	\tau_3 and \tau_4 of the Govindarajulu distribution.
ray	\tau_3 and \tau_4 of the Rayleigh distribution.
lognormal	\tau_3 and \tau_4 of the Generalized Normal (3-parameter Log-Normal) distribution.
nor	\tau_3 and \tau_4 of the Normal distribution.
pe3	\tau_3 and \tau_4 of the Pearson Type III distribution.
pdq3	\tau_3 and \tau_4 of the Polynomial Density-Quantile3 distribution.
rgov	\tau_3 and \tau_4 of the reversed Govindarajulu.
rgpa	\tau_3 and \tau_4 of the reversed Generalized Pareto.
sla	\tau^{(1)}_3 = 0 and \tau^{(1)}_4 = 0.30420472 of the Slash distribution (TL-moment [trim=1]) (see Examples lmomsla for source).
uniform	\tau_3 and \tau_4 of the uniform distribution.
wei	\tau_3 and \tau_4 of the Weibull distribution (reversed Generalized Extreme Value).

Author(s)

W.H. Asquith

References

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, \Sexpr[results=rd]{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.

See Also

plotlmrdia

Examples

lratios <- lmrdia()

lmomco documentation built on May 29, 2024, 10:06 a.m.