Fits the quantilebased Skew Logistic Distribution using LMoments.
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 usersupplied values
of the first three L Moments.
1 2  fit.sld.lmom.given(lmoms,n=NULL)
fit.sld.lmom(data)

lmoms 
A vector of length 3, containing the first and second (sample) L Moments and the 3rd (sample) L Moment ratio (tau3 ) 
n 
The sample size 
data 
A vector containing a dataset 
The method of LMoments estimates of the parameters of the quantilebased 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 LMoment, not the 3rd LMoment ratio (tau3 = L3/L2).
fit.sld.lmom
uses the samlmu
function (from
the 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.
Robert King, robert.king@newcastle.edu.au, http://tolstoy.newcastle.edu.au/~rking/ and Paul van Staden
van Staden, P.J. and King, Robert A.R. (2015) The quantilebased 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
http://tolstoy.newcastle.edu.au/rking/SLD/SLD.html
sld
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Questions? Problems? Suggestions? Tweet to @rdrrHQ or email at ian@mutexlabs.com.
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