are.pargld.valid {lmomco} | R Documentation |
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 <= F <= 1,
in which F is nonexceedance probability.
are.pargld.valid(para,verbose=FALSE,nowarn=FALSE)
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 an optimization algorithm. |
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
α(kappa F^{kappa - 1} + h(1-F)^{h -1 }) >= 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 α 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 α by
mbox{Region 1: } kappa <= -1 mbox{ and } h >= 1 mbox{,}
mbox{Region 2: } kappa >= 1 mbox{ and } h <= -1 mbox{,}
mbox{Region 3: } kappa >= 0 mbox{ and } h >= 0 mbox{,}
mbox{Region 4: } kappa <= 0 mbox{ and } h <= 0 mbox{,}
mbox{Region 5: } h >= (-1/kappa) mbox{ and } -1 >= kappa <= 0 mbox{, and}
mbox{Region 6: } h <= (-1/kappa) mbox{ and } h >= -1 mbox{ and } kappa >= 1 mbox{.}
TRUE |
If the parameters are gld consistent. |
FALSE |
If the parameters are not gld consistent. |
This function calls is.gld
to verify consistency between
the distribution parameter object and the intent of the user.
W.H. Asquith
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.
para <- vec2par(c(123,34,4,3),type='gld') if(are.pargld.valid(para)) Q <- quagld(0.5,para)