
SEMPDFName:
The probability density function for the semicircular distribution is:
with and r denoting the location and scale parameters, respectively. The scale parameter, r, is the radius of the semicircle (or ellipse if r not equal to 1). The case where = 0 and r = 1 is referred to as the standard semicircular distribution and has the following probability density function:
This distribution has mean 0 and standard deviation r/4.
<SUBSET/EXCEPT/FOR qualification> where <x> is a variable, number, or parameter; <mu> is a variable, number, or parameter that specifies the location parameter; <r> is a variable, number, or parameter that specifies the scale parameter; <y> is a variable or a parameter (depending on what <x> is) where the computed semicircular pdf value is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional. If <mu> and <r> are omitted, they default to 0 and 1, respectively.
LET A = SEMPDF(1.2,0,5) LET X2 = SEMPDF(X1)
SEMICIRCULAR PROBABILITY PLOT Y SEMICIRCULAR PROBABILITY PLOT Y2 X2 SEMICIRCULAR PROBABILITY PLOT Y3 XLOW XHIGH SEMICIRCULAR KOLMOGOROV SMIRNOV GOODNESS OF FIT Y SEMICIRCULAR CHISQUARE GOODNESS OF FIT Y2 X2 SEMICIRCULAR CHISQUARE GOODNESS OF FIT Y3 XLOW XHIGH The location and scale estimates can be obtained from the probability plot (location = PPA0 and scale = PPA1). The BOOTSTRAP DISTRIBUTION command can be used to find uncertainty intervals for the location and scale parameters based on the probability plot.
Filliben (1969), Simple and Robust Linear Estimation of the Location Parameter of a Symmetric Distribution, unpublished Ph.d dissertation, Princeton University, (pp. 2144, 229231).
2006/10: Updated to support the general case XLIMITS 1 1 XTIC OFFSET 0.1 0.1 TITLE AUTOMATIC PLOT SEMPDF(X) FOR X = 1 0.01 1
Date created: 1/8/2008 