
RPOPDFName:
with c denoting the shape 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
The reflected power distribution is a special case of the beta distribution where the first shape parameter = 1 (the power distribution is a special case of the beta distribution where the second shape parameter = 1).
<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 reflected power pdf value is stored; <c> is a positive number, parameter, or variable that specifies the shape parameter; <a> is a number, parameter, or variable that specifies the lower limit; <b> is a number, parameter, or variable that specifies the upper limit; and where the <SUBSET/EXCEPT/FOR qualification> is optional. If <a> and <b> are omitted, they default to 0 and 1, respectively.
LET Y = RPOPDF(X,0.5,0,5) PLOT RPOPDF(X,2.3) FOR X = 0 0.01 1
LET A = <value> LET B = <value> LET Y = REFLECTED POWER RANDOM NUMBERS FOR I = 1 1 N REFLECTED POWER PROBABILITY PLOT Y REFLECTED POWER PROBABILITY PLOT Y2 X2 REFLECTED POWER PROBABILITY PLOT Y3 XLOW XHIGH REFLECTED POWER KOLMOGOROV SMIRNOV GOODNESS OF FIT Y REFLECTED POWER CHISQUARE GOODNESS OF FIT Y2 X2 REFLECTED POWER CHISQUARE GOODNESS OF FIT Y3 XLOW XHIGH The following commands can be used to estimate the c shape parameter for the reflected power distribution:
LET C2 = <value> REFLECTED POWER PPCC PLOT Y REFLECTED POWER PPCC PLOT Y2 X2 REFLECTED POWER PPCC PLOT Y3 XLOW XHIGH REFLECTED POWER KS PLOT Y REFLECTED POWER KS PLOT Y2 X2 REFLECTED POWER KS PLOT Y3 XLOW XHIGH The default values for C1 and C2 are 0.5 and 25. The probability plot can then be used to estimate the lower and upper limits (lower limit = PPA0, upper limit = PPA0 + PPA1). The following options may be useful for these commands.
The BOOTSTRAP DISTRIBUTION command can be used to find uncertainty intervals for the ppcc plot, ks plot, and maximum likelihood estimates.
LABEL CASE ASIS TITLE CASE ASIS TITLE OFFSET 2 . MULTIPLOT 2 2 MULTIPLOT CORNER COORDINATES 0 0 100 95 MULTIPLOT SCALE FACTOR . LET C = 0.5 TITLE C = ^c PLOT RPOPDF(X,C) FOR X = 0 0.01 0.99 . LET C = 1 TITLE C = ^c PLOT RPOPDF(X,C) FOR X = 0 0.01 1 . LET C = 1.5 TITLE C = ^c PLOT RPOPDF(X,C) FOR X = 0 0.01 1 . LET C = 2 TITLE C = ^c PLOT RPOPDF(X,C) FOR X = 0 0.01 1 . END OF MULTIPLOT . JUSTIFICATION CENTER MOVE 50 97 TEXT Reflected Power Probability Density Functions Program 2: let c = 2.2 let y = reflected power rand numb for i = 1 1 200 . let csav = c reflected power ppcc plot y just center move 50 5 let c = shape text maxppcc = ^maxppcc, C = ^c move 50 2 text Csav = ^csav . char x line blank reflected power prob plot y move 50 5 text PPA0 = ^ppa0, PPA1 = ^ppa1 move 50 2 let upplim = ppa0 + ppa1 text Lower Limit = ^ppa0, Upper Limit = ^upplim char blank line solid . class lower 0 class upper 1 class width 0.05 relative hist y line color blue limits freeze preerase off let a = ppa0 let b = a + (ppa1  ppa0) plot rpopdf(x,c,a,b) for x = a 0.01 b limits preerase on line color black all . let ksloc = ppa0 let ksscale = upplim reflected power 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: REFLECTED POWER NUMBER OF OBSERVATIONS = 200 TEST: KOLMOGOROVSMIRNOV TEST STATISTIC = 0.3483635E01 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: 12/17/2007 