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.
The error percent point function is computed by numerically inverting the cumulative distribution function using a bisection method. For = 1 and = 2, the percent point functions for the double exponential and normal distributions, respectively, are used.
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 <p> is a variable, a number, or a parameter in the interval (0,1);
<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 <p> is) where the computed error ppf value is stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Note that the location and scale parameters are optional.
LET X2 = ERRPPF(P1,A)
PLOT ERRPPF(P,1.5) FOR X = 0.01 0.01 0.99
"Statistical Distributions", Third Edition, Evans, Hastings, and Peacock, Wiley, 2000.
"Continuous Univariate Distributions--Volume 2, Second Edition", Johnson, Kotz, and Balakrishnan, Wiley, 1994.
X1LABEL Probability Y1LABEL 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 ERRPPF(P,1) FOR P = 0.01 0.01 0.99 PLOT ERRPPF(P,1.5) FOR P = 0.01 0.01 0.99 PLOT ERRPPF(P,2) FOR P = 0.01 0.01 0.99 PLOT ERRPPF(P,4) FOR P = 0.01 0.01 0.99 END OF MULTIPLOT
Date created: 7/7/2004