
TSSPDFName:
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
<SUBSET/EXCEPT/FOR qualification> where <x> is a number, parameter, or variable containing values in the interval (a,b); <y> is a variable or a parameter (depending on what <x> is) where the computed twosided slope pdf value is stored; <alpha> is a number, parameter, or variable in the interval (0,2) that specifies the first shape parameter; <theta> is a number, parameter, or variable in the interval (a,b) that specifies the second shape parameter; <a> is a number, parameter, or variable that specifies the lower bound; <b> is a number, parameter, or variable that specifies the upper bound; and where the <SUBSET/EXCEPT/FOR qualification> is optional. If <a> and <b> are omitted, they default to 0 and 1, respectively.
LET Y = TSSPDF(X,1.5,2.2,0,5) PLOT TSSPDF(X,1.5,2.2,0,5) FOR X = 0 0.01 5
LET ALPHA = <value> LET A = <value> LET B = <value> LET Y = TWOSIDED SLOPE RANDOM NUMBERS FOR I = 1 1 N TWOSIDED SLOPE PROBABILITY PLOT Y TWOSIDED SLOPE PROBABILITY PLOT Y2 X2 TWOSIDED SLOPE PROBABILITY PLOT Y3 XLOW XHIGH TWOSIDED SLOPE KOLMOGOROV SMIRNOV GOODNESS OF FIT Y TWOSIDED SLOPE CHISQUARE GOODNESS OF FIT Y2 X2 TWOSIDED SLOPE CHISQUARE GOODNESS OF FIT Y3 XLOW XHIGH Note that
The following commands can be used to estimate the and shape parameters for the twosided slope distribution:
LET B = <value> LET THETA1 = <value> LET THETA2 = <value> LET ALPHA1 = <value> LET ALPHA2 = <value> TWOSIDED SLOPE PPCC PLOT Y TWOSIDED SLOPE PPCC PLOT Y2 X2 TWOSIDED SLOPE PPCC PLOT Y3 XLOW XHIGH TWOSIDED SLOPE KS PLOT Y TWOSIDED SLOPE KS PLOT Y2 X2 TWOSIDED SLOPE KS PLOT Y3 XLOW XHIGH Note that for the twosided slope distribution, the shape parameter is bounded by the minimum and maximum of the data. In the above commands, there are two approaches to dealing with this.
The default values for ALPHA1 and ALPHA2 are 0.05 and 2.
MULTIPLOT 3 3 MULTIPLOT CORNER COORDINATES 0 0 100 95 MULTIPLOT SCALE FACTOR 3 TITLE OFFSET 2 TITLE CASE ASIS LABEL CASE ASIS CASE ASIS . LET THETAV = DATA 0.25 0.50 0.75 LET ALPHAV = DATA 0.5 1.0 1.5 . LOOP FOR K = 1 1 3 LET THETA = THETAV(K) LOOP FOR L = 1 1 3 LET ALPHA = ALPHAV(L) TITLE Theta = ^THETA, Alpha = ^ALPHA PLOT TSSPDF(X,ALPHA,THETA) FOR X = 0 0.01 1 END OF LOOP END OF LOOP . END OF MULTIPLOT MOVE 50 97 JUSTIFICATION CENTER TEXT TwoSided Slope Probability Density Functions
let a = 0 let b = 4 let alpha = 1.3 let theta = 1.7 let alphasv = alpha let thetasv = theta . let y = twosided slope random numbers for i = 1 1 200 let ymin = minimum y let ymax = maximum y . twosided slope ppcc plot y let alpha = shape1 let theta = shape2 justification center move 50 6 text Alphahat = ^alpha, Thetahat = ^theta move 50 3 text Alpha = ^alphasv, Theta = ^thetasv . char x line bl twosided slope prob plot y move 50 6 let ahat = ppa0 let bhat = ppa0 + ppa1 let ahat = min(ahat,ymin) let bhat = max(bhat,ymax) text Lower Limit = ^ppa0, Upper Limit = ^bhat move 50 3 text PPCC = ^ppcc . two sided slope kolm smir goodness of fit y KOLMOGOROVSMIRNOV GOODNESSOFFIT TEST NULL HYPOTHESIS H0: DISTRIBUTION FITS THE DATA ALTERNATE HYPOTHESIS HA: DISTRIBUTION DOES NOT FIT THE DATA DISTRIBUTION: TWOSIDED SLOPE NUMBER OF OBSERVATIONS = 200 TEST: KOLMOGOROVSMIRNOV TEST STATISTIC = 0.4090971E01 ALPHA LEVEL CUTOFF CONCLUSION 10% 0.086* ACCEPT H0 0.085** 5% 0.096* ACCEPT H0 0.095** 1% 0.115* ACCEPT H0 0.114** *  STANDARD LARGE SAMPLE APPROXIMATION ( C/SQRT(N) ) **  MORE ACCURATE LARGE SAMPLE APPROXIMATION ( C/SQRT(N + SQRT(N/10)) )
Date created: 11/07/2007 