pargov {lmomco}

Estimate the Parameters of the Govindarajulu Distribution

Description

This function estimates the parameters of the Govindarajulu distribution given the L-moments of the data in an L-moment object such as that returned by lmoms. The relations between distribution parameters and L-moments also are seen under lmomgov. The \beta is estimated as

\beta = -\frac{(4\tau_3 + 2)}{(\tau_3 - 1)}\mbox{,}

and \alpha then \xi are estimated for unknown \xi as

\alpha = \lambda_2\frac{(\beta+2)(\beta+3)}{2\beta}\mbox{, and}

\xi = \lambda_1 - \frac{2\alpha}{(\beta+2)}\mbox{,}

and \alpha is estimated for known \xi as

\alpha = (\lambda_1 - \xi)\frac{(\beta + 2)}{2}\mbox{.}

The shape preservation for this distribution is an ad hoc decision. It could be that for given \xi, that solutions could fall back to estimating \xi and \alpha from \lambda_1 and \lambda_2 only. Such as solution would rely on \tau_2 = \lambda_2/\lambda_1 with \beta estimated as

\beta = \frac{3\tau_2}{(1-\tau_2)}\mbox{, and}

\alpha = \lambda_1\frac{(\beta+2)}{2}\mbox{,}

but such a practice yields remarkable changes in shape for this distribution even if the provided \xi precisely matches that from a previous parameter estimation for which the \xi was treated as unknown.

Usage

pargov(lmom, xi=NULL, checklmom=TRUE, ...)

Arguments

lmom

An L-moment object created by lmoms or vec2lmom.

xi

An optional lower limit of the distribution. If not NULL, the B is still uniquely determined by \tau_3, the \alpha is adjusted so that the given lower bounds is honored. It is generally accepted to let the distribution fitting process determine its own lower bounds so xi=NULL should suffice in many circumstances.

checklmom

Should the lmom be checked for validity using the are.lmom.valid function. Normally this should be left as the default and it is very unlikely that the L-moments will not be viable (particularly in the \tau_4 and \tau_3 inequality). However, for some circumstances or large simulation exercises then one might want to bypass this check.

...

Other arguments to pass.

Value

An R list is returned.

type

The type of distribution: gov.

para

The parameters of the distribution.

source

The source of the parameters: “pargov”.

Author(s)

W.H. Asquith

References

Gilchrist, W.G., 2000, Statistical modelling with quantile functions: Chapman and Hall/CRC, Boca Raton.

Nair, N.U., Sankaran, P.G., Balakrishnan, N., 2013, Quantile-based reliability analysis: Springer, New York.

Nair, N.U., Sankaran, P.G., and Vineshkumar, B., 2012, The Govindarajulu distribution—Some Properties and applications: Communications in Statistics, Theory and Methods, v. 41, no. 24, pp. 4391–4406.

See Also

lmomgov, cdfgov, pdfgov, quagov

Examples

lmr <- lmoms(rnorm(20))
pargov(lmr)

lmr <- vec2lmom(c(1391.8, 215.68, 0.01655, 0.09628))
pargov(lmr)$para             # see below
#         xi       alpha        beta 
# 868.148125 1073.740595    2.100971 
pargov(lmr, xi=868)$para     # see below
#         xi       alpha        beta 
# 868.000000 1074.044324    2.100971 
pargov(lmr, xi=100)$para     # see below
#         xi       alpha        beta 
# 100.000000 2648.817215    2.100971