qualn3: Quantile Function of the 3-Parameter Log-Normal Distribution

In wasquith/lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

Quantile Function of the 3-Parameter Log-Normal Distribution

Description

This function computes the quantiles of the Log-Normal3 distribution given parameters (\zeta, lower bounds; \mu_{\mathrm{log}}, location; and \sigma_{\mathrm{log}}, scale) of the distribution computed by parln3. The quantile function (same as Generalized Normal distribution, quagno) is

x = \Phi^{(-1)}(Y) \mbox{,}

where \Phi^{(-1)} is the quantile function of the Standard Normal distribution and Y is

Y = \frac{\log(x - \zeta) - \mu_{\mathrm{log}}}{\sigma_{\mathrm{log}}}\mbox{,}

where \zeta is the lower bounds (real space) for which \zeta < \lambda_1 - \lambda_2 (checked in are.parln3.valid), \mu_{\mathrm{log}} be the mean in natural logarithmic space, and \sigma_{\mathrm{log}} be the standard deviation in natural logarithm space for which \sigma_{\mathrm{log}} > 0 (checked in are.parln3.valid) is obvious because this parameter has an analogy to the second product moment. Letting \eta = \exp(\mu_{\mathrm{log}}), the parameters of the Generalized Normal are \zeta + \eta, \alpha = \eta\sigma_{\mathrm{log}}, and \kappa = -\sigma_{\mathrm{log}}. At this point, the algorithms (quagno) for the Generalized Normal provide the functional core.

Usage

qualn3(f, para, paracheck=TRUE)

Arguments

f	Nonexceedance probability (0 \le F \le 1).
para	The parameters from parln3 or vec2par.
paracheck	A logical controlling whether the parameters are checked for validity. Overriding of this check might be extremely important and needed for use of the distribution quantile function in the context of TL-moments with nonzero trimming.

Value

Quantile value for nonexceedance probability F.

Note

The parameterization of the Log-Normal3 results in ready support for either a known or unknown lower bounds. More information regarding the parameter fitting and control of the \zeta parameter can be seen in the Details section under parln3.

Author(s)

W.H. Asquith

References

Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: Createspace Independent Publishing Platform, ISBN 978–146350841–8.

See Also

cdfln3, pdfln3, lmomln3, parln3, quagno

Examples

  lmr <- lmoms(c(123,34,4,654,37,78))
  qualn3(0.5,parln3(lmr))

wasquith/lmomco documentation built on Nov. 13, 2024, 4:53 p.m.