
ALPCDFName:
with denoting the shape parameter. This distribution can be generalized with location and scale parameters using the relation
If Y has a normal distribution with location and scale parameters and truncated to the left of 0, then X = 1/Y has an alpha distribution with shape parameter = / and scale parameter . This distribution has application in reliability.
<SUBSET/EXCEPT/FOR qualification> where <x> is a number, parameter, or variable containing positive values; <y> is a variable or a parameter (depending on what <x> is) where the computed alpha cdf value is stored; <alpha> is a positive number, parameter, or variable that specifies the shape parameter; <loc> is a number, parameter, or variable that specifies the location parameter; <scale> is a positive number, parameter, or variable that specifies the scale parameter; and where the <SUBSET/EXCEPT/FOR qualification> is optional. If <loc> and <scale> are omitted, they default to 0 and 1, respectively.
LET A = ALPCDF(X1,2.5,0,10) PLOT ALPCDF(X,2.5,0,3) FOR X = 0.1 0.1 10
to
This was done since BETA is in fact a scale parameter.
Salvia (1985), "Reliability applications of the Alpha Distribution", IEEE Transactions on Reliability, Vol. R34, No. 3, pp. 251252.
2007/11: Corrected the second shape parameter to be the scale parameter LABEL CASE ASIS TITLE CASE ASIS TITLE OFFSET 2 . MULTIPLOT 2 2 MULTIPLOT CORNER COORDINATES 0 0 100 95 MULTIPLOT SCALE FACTOR 2 . LET ALPHA = 0.5 TITLE ALPHA = ^alpha PLOT ALPCDF(X,ALPHA) FOR X = 0.01 0.01 5 . LET ALPHA = 1 TITLE ALPHA = ^alpha PLOT ALPCDF(X,ALPHA) FOR X = 0.01 0.01 5 . LET ALPHA = 2 TITLE ALPHA = ^alpha PLOT ALPCDF(X,ALPHA) FOR X = 0.01 0.01 5 . LET ALPHA = 5 TITLE ALPHA = ^alpha PLOT ALPCDF(X,ALPHA) FOR X = 0.01 0.01 5 . END OF MULTIPLOT . JUSTIFICATION CENTER MOVE 50 97 TEXT Alpha Cumulative Distribution Functions
Date created: 11/27/2007 