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. Syntax:
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 L-Moments", IBM Research Division, T. J. Watson Research Center, Yorktown Heights, NY 10598.
Hoskings (1990), "L-moments: Analysis and Estimation of Distribution using Linear Combinations of Order Statistics", Journal of the Royal Statistical Society, Series B, 52, pp. 105-124.
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