with n denoting the shape parameter.
The cumulative distribution function is computed by numerically integrating the probability density function. The percent point function is computed by numerically inverting the cumulative distribution function.
This distribution can be extended with lower and upper bound parameters. If a and b denote the lower and upper bounds, respectively, then the location and scale parameters are:
scale = b - a
The general form of the distribution can then be found by using the relation
where <p> is a number, parameter, or variable containing values in the interval (0,1);
<y> is a variable or a parameter (depending on what <p> is) where the computed ogive ppf value is stored;
<n> is a positive number, parameter, or variable that specifies the shape parameter;
<a> is a number, parameter, or variable that specifies the lower limit;
<b> is a number, parameter, or variable that specifies the upper limit;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
If <a> and <b> are omitted, they default to 0 and 1, respectively.
LET Y = OGIPPF(P,2.5,0,5)
PLOT OGIPPF(P,2,0,3) FOR P = 0 0.01 1
LABEL CASE ASIS TITLE CASE ASIS TITLE OFFSET 2 . MULTIPLOT 2 2 MULTIPLOT CORNER COORDINATES 0 0 100 95 MULTIPLOT SCALE FACTOR 2 . LET N = 0.5 TITLE N = ^n PLOT OGIPPF(P,N) FOR P = 0 0.01 1 . LET N = 0.8 TITLE N = ^n PLOT OGIPPF(P,N) FOR P = 0 0.01 1 . LET N = 1.5 TITLE N = ^n PLOT OGIPPF(P,N) FOR P = 0 0.01 1 . LET N = 2 TITLE N = ^n PLOT OGIPPF(P,N) FOR P = 0 0.01 1 . END OF MULTIPLOT . JUSTIFICATION CENTER MOVE 50 97 TEXT Ogive Cumulative Distribution Functions
Date created: 11/07/2007