Fits the quantile-based Skew Logistic Distribution using L-Moments.
fit.sld.lmom calculates the sample L Moments of a dataset and uses the
method of L Moments to estimate the parameters of the skew logistic distribution.
fit.sld.lmom.given fits the skew logistic using user-supplied values
of the first three L Moments.
A vector of length 3, containing the first and second (sample) L Moments and the 3rd (sample) L Moment ratio (tau3 )
The sample size
A vector containing a dataset
The method of L-Moments estimates of the parameters of the quantile-based skew logistic distribution are:
alpha = L1 - 6L3
beta = 2 L2
delta = 0.5*(1+3*tau3)
Note that L3 in the alpha estimate is the 3rd L-Moment, not the 3rd L-Moment ratio (tau3 = L3/L2).
fit.sld.lmom uses the
samlmu function (from
lmom package) to calculate the sample L moments, then
fit.sld.lmom.given to calculate the estimates.
If the sample size is unknown (via using
fit.sld.lmom.given and not specifying the sample size), a vector of length 3, with the estimated parameters,
alpha, beta and delta.
If the sample size is known, a 3 by 2 matrix. The first column contains the estimated parameters, alpha, beta and delta, and the second column provides asymptotic standard errors for these.
Note that if abs(tau3) > 1/3, delta hat is beyond its allowed value of [0,1] and the function returns an error. Values of abs(tau3), beyond 1/3 correspond to distributions with greater skew than the exponential / reflected exponential, which form the limiting cases of the skew logistic distribution.
van Staden, P.J. and King, Robert A.R. (2015) The quantile-based skew logistic distribution, Statistics and Probability Letters 96 109–116. http://dx.doi.org/10.1016/j.spl.2014.09.001
van Staden, Paul J. 2013 Modeling of generalized families of probability distribution in the quantile statistical universe. PhD thesis, University of Pretoria. http://hdl.handle.net/2263/40265
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