lmomco (version 0.88)

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

Description

The distribution parameter object returned by functions of this package such as by vec2par are consistent with the corresponding distribution, otherwise a list would not have been returned. However, other functions (quagld) require consistent parameters to ensure that the Generalized Lambda Distribution is monotonic increasing on $0 \le F \le 1$, in which $F$ is nonexceedance probability.

Usage

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

Arguments

para

A distribution parameter list returned by vec2par.

verbose

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

nowarn

A logical switch on warning surpression. 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 a

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

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

Examples

para <- vec2par(c(123,34,4,3),type='gld')
if(are.pargld.valid(para)) Q <- quagld(0.5,para)