lmomco (version 2.0.1)

lmomst3: L-moments of the 3-Parameter Student T Distribution

Description

This function estimates the first six L-moments of the 3-parameter Student T distribution given the parameters ($\xi$, $\alpha$, $\nu$) from parst3. The parameter $\tau_4(\nu)$ was solved numerically and a polynomial approximation made. The polynomial in turn with a root-solver is used to solve $\nu(\tau_4)$ in parst3. The other two parameters are readily solved for when $\nu$ is available. The polynomial based on $\log{\tau_4}$ and $\log{\nu}$ has nine coefficients with a residual standard error (in natural logarithm units of $\tau_4$) of 0.0001565 for 3250 degrees of freedom and an adjusted R-squared of 1. A polynomial approximation is used to estimate the $\tau_6$ as a function of $\tau_4$; the polynomial was based on the theoLmoms estimating $\tau_4$ and $\tau_6$. The $\tau_6$ polynomial has nine coefficients with a residual standard error units of $\tau_6$ of 1.791e-06 for 3593 degrees of freedom and an adjusted R-squared of 1.

Usage

lmomst3(para, bypoly=TRUE)

Arguments

para

The parameters of the distribution.

bypoly

A logical as to whether a polynomial approximation of $\tau_4$ as a function of $\nu$ will be used. The default is TRUE because this polynomial is used to reverse the estimate for $\nu$ as a function of $\tau_4$. A polynomial of $\tau_6(\tau_

Value

• An R list is returned.

References

Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: CreateSpace Independent Publishing Platform, 2nd printing, ISBN 978-1463508418.

See Also

cdfst3, parst3, pdfst3, quast3

Examples

lmomst3(vec2par(c(1124,12.123,10), type="st3"))