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TSOPDFName:
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with n denoting the shape parameter and
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
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Kotz and Van Dorp note that the two-sided ogive distribution
is smooth at the reflection point (x =
<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 two-sided 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 = TWO-SIDED SLOPE RANDOM NUMBERS FOR I = 1 1 N TWO-SIDED SLOPE PROBABILITY PLOT Y TWO-SIDED SLOPE PROBABILITY PLOT Y2 X2 TWO-SIDED SLOPE PROBABILITY PLOT Y3 XLOW XHIGH TWO-SIDED SLOPE KOLMOGOROV SMIRNOV GOODNESS OF FIT Y TWO-SIDED SLOPE CHI-SQUARE GOODNESS OF FIT Y2 X2 TWO-SIDED SLOPE CHI-SQUARE GOODNESS OF FIT Y3 XLOW XHIGH Note that
The following commands can be used to estimate the n and
LET B = <value> LET THETA1 = <value> LET THETA2 = <value> LET N1 = <value> LET N2 = <value> TWO-SIDED SLOPE PPCC PLOT Y TWO-SIDED SLOPE PPCC PLOT Y2 X2 TWO-SIDED SLOPE PPCC PLOT Y3 XLOW XHIGH TWO-SIDED SLOPE KS PLOT Y TWO-SIDED SLOPE KS PLOT Y2 X2 TWO-SIDED SLOPE KS PLOT Y3 XLOW XHIGH
Note that for the two-sided ogive distribution, the
shape parameter
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 Two-Sided Ogive Probability Density Functions let n = 2.3 let theta = 2.5 let a = 0 let b = 5 let nsv = n let thetasv = theta . let y = two-sided 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 two-sided 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 two-sided 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 = (b-a) two-sided ogive kolm smir goodness of fit y . relative hist y line color blue limits freeze pre-erase off plot tsopdf(x,n,theta,a,b) for x = a 0.01 b limits pre-erase on line color black all ![]()
Date created: 12/13/2007 |