sld (version 1.0.0)

fit.sld.lmom: Fit the skew logistic distribution using L-Moments

Description

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.

Usage

fit.sld.lmom.given(lmoms,n=NULL)
fit.sld.lmom(data)

Arguments

lmoms

A vector of length 3, containing the first and second (sample) L Moments and the 3rd (sample) L Moment ratio (\(\tau_3\))

n

The sample size

data

A vector containing a dataset

Value

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, \(\hat\alpha\), \(\hat\beta\) and \(\hat\delta\).

If the sample size is known, a 3 by 2 matrix. The first column contains the estimated parameters, \(\hat\alpha\), \(\hat\beta\) and \(\hat\delta\), and the second column provides asymptotic standard errors for these.

Note that if \(|\tau_3| > \frac 13\), \(\hat\delta\) is beyond its allowed value of [0,1] and the function returns an error. Values of \(|\tau_3|\), beyond \(\frac 13\) correspond to distributions with greater skew than the exponential / reflected exponential, which form the limiting cases of the skew logistic distribution.

Details

The method of L-Moments estimates of the parameters of the quantile-based skew logistic distribution are: $$\hat\alpha=L_1 - 6 L_3$$ $$\hat\beta = 2 L_2$$ $$\hat\delta= \frac 12 \left( 1 + 3\tau_3\right)$$ Note that \(L_3\) in the \(\hat\alpha\) estimate is the 3rd L-Moment, not the 3rd L-Moment ratio (\(\tau_3 = L_3/L_2\)).

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.

References

van Staden, P.J. and King, Robert A.R. (2015) The quantile-based skew logistic distribution, Statistics and Probability Letters 96 109--116. 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

See Also

sld

Examples

# NOT RUN {
generated.data <- rsl(300,c(0,1,.4))
estimate1 <- fit.sld.lmom(generated.data)
estimate2 <- fit.sld.lmom.given(c(0,1,.3),n=300)
data(PCB1)
hist(PCB1,prob=TRUE,main="PCB in Pelican Egg Yolk with SLD fit")
fit.pcb <- fit.sld.lmom(PCB1)
print(fit.pcb)
plotsld(fit.pcb[,1],add=TRUE,col="blue")
# }