Dataplot Vol 2 Auxiliary Chapter

NORMXPPF

Name:
    NORMXPPF (LET)
Type:
    Library Function
Purpose:
    Compute the percent point function of a mixture of two normal distributions.
Description:
    The normal mixture distribution has the following cumulative distribution function:

      F(x,u1,sd1,u2,sd2,p)=p*norcdf(u1,sd1) +
 (1-p)*norcdf(u2,sd2)

    where norcdf(u,s) is a normal probability density function with mean u and standard deviation s, p is a real number between 0 and 1 that defines the mixing proportions, and x is a real number.

    The percent point function is the inverse of the cumulative distribution function. That is, given a probability value, it returns the corresponding x value. The percent point function for the mixture of two normal distributions is computed numerically.

Syntax:
    LET <y2> = NORMXPPF(<p>,<u1>,<sd1>, <u2>,<sd2>,<pmix>)
                            <SUBSET/EXCEPT/FOR qualification>
    where <p> is a number, parameter, or variable containing probability values between 0 and 1;
    <u1> is a number, parameter, or variable;
                <sd1> is a number, parameter, or variable;
                <u2> is a number, parameter, or variable;
                <sd2> is a number, parameter, or variable;
                <pmix> is a number, parameter, or variable in the range 0 to 1;
                <y2> is a variable or a parameter (depending on what <p> is) where the computed normal mixture ppf value is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = NORMXPPF(0.95,0,1,10,20,0.2)
    LET A = NORMXPPF(0.90,U1,SD1,U2,SD2,P)
    LET Y = NORMXPPF(P,U1,SD1,U2,SD2,PMIX)
Note:
    You can generate a probability plot for a normal mixture distribution as follows:

      LET U1 = <value>
      LET SD1 = <value>
      LET U2 = <value>
      LET SD2 = <value>
      LET P = <value>
      NORMAL MIXTURE PROBABILITY PLOT Y

    You can generate random numbers from a normal mixture distribution as follows:

      LET U1 = <value>
      LET SD1 = <value>
      LET U2 = <value>
      LET SD2 = <value>
      LET P = <value>
      LET Y = NORMAL MIXTURE RANDOM NUMBERS FOR I = 1 1 1000
Default:
    None
Synonyms:
    None
Related Commands:
    NORMXPDF = Compute the normal mixture probability density function.
    NORMXCDF = Compute the normal mixture cumulative distribution function.
    NORCDF = Compute the normal cumulative distribution function.
    NORPDF = Compute the normal probability density function.
    NORPPF = Compute the normal percent point function.
Reference:
    "Continuous Univariate Distributions: Volume 1", Johnson, Kotz, and Balakrishnan, John Wiley and Sons, 1994.
Applications:
    Distributional Modeling
Implementation Date:
    1998/5
Program:
    MULTIPLOT 2 2
    MULTIPLOT CORNER COORDINATES 5 5 95 95
    YLIMITS -5 15
    XLIMITS 0 1
    MAJOR XTIC MARK NUMBER 6
    MINOR XTIC MARK NUMBER 1
    LET U1 = 0
    LET SD1 = 1
    LET U2 = 5
    LET SD2 = 3
    TITLE P = 0.2
    PLOT NORMXPPF(P,U1,SD1,U2,SD2,0.2) FOR P = 0.01 0.01 0.99
    TITLE P = 0.4
    PLOT NORMXPPF(P,U1,SD1,U2,SD2,0.4) FOR P = 0.01 0.01 0.99
    TITLE P = 0.6
    PLOT NORMXPPF(P,U1,SD1,U2,SD2,0.6) FOR P = 0.01 0.01 0.99
    TITLE P = 0.8
    PLOT NORMXPPF(P,U1,SD1,U2,SD2,0.8) FOR P = 0.01 0.01 0.99
    END OF MULTIPLOT

    plot generated by sample program

Date created: 6/5/2001
Last updated: 4/4/2003
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