KAPPPF

KAPPPF (LET)

Library Function

Compute the kappa percent point function with shape parameters h and k.

The general form of the kappa distribution has the following percent point function:

with k and h denoting the shape parameters and and denoting the location and scale parameters, respectively.

The standard form of the distribution is defined as = 0 and = 1.

LET <y> = KAPPPF(<p>,<k>,<h>,<xi>,<alpha>)
                        <SUBSET/EXCEPT/FOR qualification>
where <p> is a number, parameter, or variable in the range (0,1);
            <k> is a number, parameter, or variable that specifies the first shape parameter;
            <h> is a number, parameter, or variable that specifies the second shape parameter;
            <xi> is a number, parameter, or variable that specifies the location parameter;
            <alpha> is a number, parameter, or variable that specifies the scale parameter;
            <y> is a variable or a parameter (depending on what <x> is) where the computed kappa ppf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

The <xi> and <alpha> parameters are optional.

LET A = KAPPPF(0.95,0.5,2,0,1.5)
LET X2 = KAPPPF(P1,K,H)

Dataplot uses Hoskings QUAKAP routine to compute the kappa percent point function. Hoskings report and associated Fortran code can be downloaded from the Statlib archive at
http://lib.stat.cmu.edu/

None

None

KAPCDF	= Compute the kappa cumulative distribution function.
KAPDPF	= Compute the kappa probability density function.
MIEPDF	= Compute Miekle's beta-kappa probability density function.
GEVPDF	= Compute the generalized extreme value probability density function.
GEPPDF	= Compute the generalized Pareto probability density function.
GL5PDF	= Compute the Hosking's generalized logistic probability density function.

Hosking and Wallis (1997), "Regional Frequency Analysis", Cambridge University Press, Appendix A10.

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.

Distributional Modeling

2008/5

 
LET KP = DATA -0.5  0.1  0.5  1.0
LET H1 = -0.5
LET H2 = 0.1
LET H3 = 1
LET H4 = 2
.
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 95 95
MULTIPLOT SCALE FACTOR 2
TITLE CASE ASIS
TITLE OFFSET 2
X3LABEL
LINE COLOR BLACK RED BLUE GREEN
.
LOOP FOR KK = 1 1 4
   LET K = KP(KK)
   TITLE K = ^K, H = -0.5, 0.1, 1, 2
   PLOT KAPPPF(P,K,H1) FOR P = 0.02  0.01  0.98  AND
   PLOT KAPPPF(P,K,H2) FOR P = 0.02  0.01  0.98  AND
   PLOT KAPPPF(P,K,H3) FOR P = 0.02  0.01  0.98  AND
   PLOT KAPPPF(P,K,H4) FOR P = 0.02  0.01  0.98
END OF LOOP
END OF MULTIPLOT
.
CASE ASIS
JUSTIFICATION CENTER
MOVE 50 97
TEXT Kappa PPF Functions