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Dataplot Vol 2 Vol 1

GTRPPF

Name:
    GTRPPF (LET)
Type:
    Library Function
Purpose:
    Compute the generalized trapezoidal percent point function.
Description:
    The generalized trapezoidal distribution has the following cumulative distribution function:

      F(x|a,b,c,d,nu1,nu3,alpha) = 0 x < a; 2*alpha*(b-a)*nu3*((x-a)/(b-a))**nu1/ [2*alpha*(b-a)*nu3+(alpha+1)*(c-b)*nu1*nu3+2*(d-c)*nu1] a <= x < b; 2*alpha*(b-a)*nu3+2*(x-b)*nu1*nu3* [1 + ((alpha-1)/2)*((2*c-b-x)/(c-b))]/ [2*alpha*(b-a)*nu3+(alpha+1)*(c-b)*nu1*nu3+2*(d-c)*nu1] b <= x < c; 1 - {2*(d-c)*nu1*((d-x)/(d-c))**nu3/ [2*alpha*(b-a)*nu3+(alpha+1)*(c-b)*nu1*nu3+2*(d-c)*nu1]} c <= x < d; 1 x >= d

    The algorithm for the generalized trapezoid percent point function is to compute the cumulative distribution function at the points a, b, c, and d to determine an appropriate bracketing interval. Then the appropriate equation above is inverted to find the value of the percent point function. For the interval b <= x < c, a bisection method is used.

Syntax:
    LET <y> = GTRPPF(<p>,<a>,<b>,<c> <d>,<nu1>,<nu3>,<alpha>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <x> is a variable, number, or parameter containing values in the interval (a,d);
                <a> is a number, parameter, or variable that specifies the first shape parameter;
                <b> is a number, parameter, or variable that specifies the second shape parameter;
                <c> is a number, parameter, or variable that specifies the third shape parameter;
                <d> is a number, parameter, or variable that specifies the fourth shape parameter;
                <nu1> is a number, parameter, or variable that specifies the fifth shape parameter;
                <nu3> is a number, parameter, or variable that specifies the sixth shape parameter;
                <alpha> is a number, parameter, or variable that specifies the seventh shape parameter;
                <y> is a variable or a parameter (depending on what <p> is) where the computed ppf value is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = GTRPPF(0.95,0,0.2,0.8,1,2,2,0.5)
    LET Y = GTRPPF(P,0,0.2,0.8,1,2,2,0.5)
    LET Y = GTRPPF(P,A,B,C,D,NU1,NU3,ALPHA)
Default:
    None
Synonyms:
    None
Related Commands:
    GTRCDF = Compute the generalized trapezoidal cumulative distribution function.
    GTRPDF = Compute the generalized trapezoidal probability density function.
    TRAPDF = Compute the trapezoidal probability density function.
    TRIPDF = Compute the triangular probability density function.
    UNIPDF = Compute the uniform probability density function.
    SEMPDF = Compute the semi-circular probability density function.
    NORPDF = Compute the normal probability density function.
Reference:
    "Generalized Trapezoidal Distributions", van Dorp and Kotz, Metrika, Vol. 58, Issue 1, July, 2003.
Applications:
    Distributional Modeling
Implementation Date:
    2004/1
Program: 
     
TITLE GENERALIZED TRAPEZOIDAL DISTRIBUTION
LABEL CASE ASIS
X1LABEL Probability
Y1LABEL X
LET A = 0
LET B = 0.2
LET C = 0.8
LET D = 1
LET NU1 = 1.5
LET NU3 = 2.2
LET ALPHA = 0.5
PLOT GTRPPF(P,A,B,C,D,NU1,NU3,ALPHA) FOR P = 0  0.01  1
    plot generated by sample program

Date created: 2/3/2004
Last updated: 2/3/2004
Please email comments on this WWW page to alan.heckert@nist.gov.