
TSOPDFName:
with n denoting the shape parameter and denoting the reflection parameter. 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
Kotz and Van Dorp note that the twosided ogive distribution is smooth at the reflection point (x = ). This is in contrast to the twosided slope and twosided power distributions, which are not smooth at the relection point.
<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 ogive pdf value is stored; <n> is a number, parameter, or variable in the interval (≥ 0.5) 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 = TSOPDF(X,1.5,2.2,0,5) PLOT TSOPDF(X,1.5,2.2,0,5) FOR X = 0 0.01 5
LET N = <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 n and shape parameters for the twosided ogive distribution:
LET B = <value> LET THETA1 = <value> LET THETA2 = <value> LET N1 = <value> LET N2 = <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 ogive 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 N1 and N2 are 0.05 and 10.
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 NV = DATA 0.5 1.0 1.5 . LOOP FOR K = 1 1 3 LET THETA = THETAV(K) LOOP FOR L = 1 1 3 LET N = NV(L) TITLE Theta = ^THETA, Alpha = ^N PLOT TSOPDF(X,N,THETA) FOR X = 0 0.01 1 END OF LOOP END OF LOOP . END OF MULTIPLOT MOVE 50 97 JUSTIFICATION CENTER TEXT TwoSided Ogive Probability Density FunctionsProgram 2: let n = 2.3 let theta = 2.5 let a = 0 let b = 5 let nsv = n let thetasv = theta . let y = twosided ogive rand numb for i = 1 1 200 let ymin = minimum y let ymax = maximum y . let theta1 = 1.5 let theta2 = 4 let n1 = 1.1 let n2 = 5 twosided ogive ppcc plot y let n = shape1 let theta = shape2 justification center move 50 6 text Thetahat = ^theta, ^Nhat = ^n move 50 3 text Theta = ^thetasv, N = ^Nsv . character x line bl twosided ogive probability plot y let a = ppa0 let b = ppa0 + ppa1 let a = min(a,ymin) let b = max(b,ymax) move 50 6 text Lower Limit = ^a, Upper Limit = ^b move 50 3 text PPCC = ^ppcc char bl line so . let ksloc = ppa0 let ksscale = (ba) twosided ogive kolm smir goodness of fit y . relative hist y line color blue limits freeze preerase off plot tsopdf(x,n,theta,a,b) for x = a 0.01 b limits preerase on line color black all
KOLMOGOROVSMIRNOV GOODNESSOFFIT TEST NULL HYPOTHESIS H0: DISTRIBUTION FITS THE DATA ALTERNATE HYPOTHESIS HA: DISTRIBUTION DOES NOT FIT THE DATA DISTRIBUTION: TWOSIDED OGIVE NUMBER OF OBSERVATIONS = 200 TEST: KOLMOGOROVSMIRNOV TEST STATISTIC = 0.8571517E01 ALPHA LEVEL CUTOFF CONCLUSION 10% 0.086* REJECT 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: 12/13/2007 