
WAKCDFName:
where U is a standard uniform random variable. That is, the above equation defines the percent point function for the Wakeby distribution. The parameters , and are shape parameters. The parameter is a location parameter and the parameter is a scale parameter. The following restrictions apply to the parameters of this distribution:
The domain of the Wakeby distribution is
With three shape parameters, the Wakeby distribution can model a wide variety of shapes. The cumulative distribution function is computed by numerically inverting the percent point function given above.
<SUBSET/EXCEPT/FOR qualification> where <x> is a number, parameter, or variable; <y> is a variable or a parameter (depending on what <x> is) where the computed Wakeby cdf value is stored; <beta> is a number, parameter, or variable that specifies the first shape parameter; <gamma> is a number, parameter, or variable that specifies the second shape parameter; <delta> is a number, parameter, or variable that specifies the third shape parameter; <chi> is a number, parameter, or variable that specifies the location parameter; <alpha> is a number, parameter, or variable that specifies the scale parameter; and where the <SUBSET/EXCEPT/FOR qualification> is optional. If <xi> and <alpha> are omitted, they default to 0 and 1, respectively.
LET A = WAKCDF(13,2.5,6,0,10) PLOT WAKCDF(X,2.5,6) FOR X = 10 0.1 10
Hoskings report and associated Fortran code can be downloaded from the Statlib archive at
J. R. M. Hosking (2000), "Research Report: Fortran Routines for use with the Method of LMoments", IBM Research Division, T. J. Watson Research Center, Yorktown Heights, NY 10598. Hoskings (1990), "Lmoments: Analysis and Estimation of Distribution using Linear Combinations of Order Statistics", Journal of the Royal Statistical Society, Series B, 52, pp. 105124.
let xi = 0 let alpha = 10 let beta = 5 let gamma = 1 let delta = 0.3 . plot wakcdf(x,beta,gamma,delta,xi,alpha) for x = .01 .01 15
Date created: 12/17/2007 