Dataplot supports another distribution that is also called the exponential power distribution. This is a different distribution than the one described here (enter HELP PEXPDF for details).
The standard error distribution has the following probability density function:
with and denoting the gamma function (HELP GAMMA for details) and the shape parameter, respectively.
For x > 0, Dataplot computes the error cdf function with the following formula:
with denoting the gamma function (HELP GAMMA for details), denoting the incomplete gamma function (HELP GAMMAI for details), and denoting the shape parameter. Negative values of x are computed by using the above formula for positive x and taking advantage of the symmetry of the error distribution.
For = 1 and = 2, the error distribution is equivalent to the double exponential and normal distribution, respectively. As goes to infinity, the error distribution approximates a uniform distribution. For applications, values of between 1 and 6 are typically of most interest. The error distribution is sometimes used in simulation studies because it provides a symmetric distribution with widely varying kurtosis.
The error distribution can be generalized with location and scale parameters in the usual way.
where <x> is a variable, a number, or a parameter;
<alpha> is a number or parameter specifying the shape parameter;
<loc> is a number or parameter that specifies the value of the location parameter;
<scale> is a number or parameter that specifies the value of the scale parameter;
<y> is a variable or a parameter (depending on what <x> is) where the computed error cdf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Note that the location and scale parameters are optional.
LET X2 = ERRCDF(X1,A)
PLOT ERRCDF(X,1.5) FOR X = -3 0.01 3
"Statistical Distributions", Third Edition, Evans, Hastings, and Peacock, Wiley, 2000.
"Continuous Univariate Distributions--Volume 2, Second Edition", Johnson, Kotz, and Balakrishnan, Wiley, 1994.
Y1LABEL Probability X1LABEL X LABEL CASE ASIS X1LABEL DISPLACEMENT 12 Y1LABEL DISPLACEMENT 12 MULTIPLOT 2 2 MULTIPLOT CORNER COORDINATES 0 0 100 100 MULTIPLOT SCALE FACTOR 2 TITLE AUTOMATIC PLOT ERRCDF(X,1) FOR X = -5 0.01 5 PLOT ERRCDF(X,1.5) FOR X = -5 0.01 5 PLOT ERRCDF(X,2) FOR X = -5 0.01 5 PLOT ERRCDF(X,4) FOR X = -5 0.01 5 END OF MULTIPLOT
Date created: 7/7/2004