lmomco (version 2.3.1)

are.pargld.valid: Are the Distribution Parameters Consistent with the Generalized Lambda Distribution

Description

Is the distribution parameter object consistent with the corresponding distribution? The distribution functions (cdfgld, pdfgld, quagld, and lmomgld) require consistent parameters to return the cumulative probability (nonexceedance), density, quantile, and L-moments of the distribution, respectively. These functions internally use the are.pargld.valid function.

Usage

are.pargld.valid(para, verbose=FALSE, nowarn=FALSE)

Arguments

para

A distribution parameter list returned by pargld or vec2par.

verbose

A logical switch on additional output to the user---default is FALSE.

nowarn

A logical switch on warning suppression. If TRUE then options(warn=-1) is made and restored on return. This switch is to permit calls in which warnings are not desired as the user knows how to handle the returned value---say in an optimization algorithm.

Value

TRUE

If the parameters are gld consistent.

FALSE

If the parameters are not gld consistent.

Details

Karian and Dudewicz (2000) outline valid parameter space of the Generalized Lambda distribution. First, according to Theorem 1.3.3 the distribution is valid if and only if $$\alpha(\kappa F^{\kappa - 1} + h(1-F)^{h -1 }) \ge 0 \mbox{.}$$ for all \(F \in [0,1]\). The are.pargld.valid function tests against this condition by incrementing through \([0,1]\) by \(dF = 0.0001\). This is a brute force method of course. Further, Karian and Dudewicz (2002) provide a diagrammatic representation of regions in \(\kappa\) and \(h\) space for suitable \(\alpha\) in which the distribution is valid. The are.pargld.valid function subsequently checks against the 6 valid regions as a secondary check on Theorem 1.3.3. The regions of the distribution are defined for suitably choosen \(\alpha\) by

$$\mbox{Region 1: } \kappa \le -1 \mbox{ and } h \ge 1 \mbox{,}$$ $$\mbox{Region 2: } \kappa \ge 1 \mbox{ and } h \le -1 \mbox{,}$$ $$\mbox{Region 3: } \kappa \ge 0 \mbox{ and } h \ge 0 \mbox{,}$$ $$\mbox{Region 4: } \kappa \le 0 \mbox{ and } h \le 0 \mbox{,}$$ $$\mbox{Region 5: } h \ge (-1/\kappa) \mbox{ and } -1 \ge \kappa \le 0 \mbox{, and}$$ $$\mbox{Region 6: } h \le (-1/\kappa) \mbox{ and } h \ge -1 \mbox{ and } \kappa \ge 1 \mbox{.}$$

References

Asquith, W.H., 2007, L-moments and TL-moments of the generalized lambda distribution: Computational Statistics and Data Analysis, v. 51, no. 9, pp. 4484--4496.

Karian, Z.A., and Dudewicz, E.J., 2000, Fitting statistical distributions---The generalized lambda distribution and generalized bootstrap methods: CRC Press, Boca Raton, FL, 438 p.

See Also

is.gld, pargld

Examples

# NOT RUN {
para <- vec2par(c(123,34,4,3),type='gld')
if(are.pargld.valid(para)) Q <- quagld(0.5,para)

# The following is an example of inconsistent L-moments for fitting but
# prior to lmomco version 2.1.2 and untrapped error was occurring.
lmr <- lmoms(c(33, 37, 41, 54, 78, 91, 100, 120, 124))
para <- pargld(lmr); are.pargld.valid(para)
# }