/* pdfncf.sas */ /* */ /* compute non-central F probability */ options ls=80 ; data a ; input ndf ddf calph ; /* for several noncentrality values */ do phi = 0 to 14 by 2 ; /* */ /* first use SAS function */ /* note different noncentrality def */ p1 = probf(calph,ndf,ddf,2*phi) ; /* ********/ /* do zero case of poisson sum */ poisprj = exp(-phi) ; * start poisson probs ; p2 = poisprj*probf(calph,ndf,ddf) ; do j = 1 to 39 ; * hope that's enough ; poisprj = poisprj*phi/j ; p2 = p2 + poisprj*probf(calph*ndf/(ndf+2*j),2*j+ndf,ddf) ; end ; /* done with poisson weighted sum */ output ; /* end of phi loop */ end ; cards ; 4 4 4.11 .90 3 5 3.62 .90 3 5 7.76 .975 4 5 3.52 .90 4 5 7.39 .975 3 6 3.29 .90 3 6 6.60 .975 4 6 3.18 .90 4 6 6.23 .975 6 10 3.22 .95 ; run ; proc print data=a ; var ndf ddf phi p1 p2 ; title 'some non-central F probabilities' ; run ; some non-central F probabilities 1 16:56 Tuesday, March 25, 2008 Obs ndf ddf phi p1 p2 1 4 4 0 0.90010 0.90010 2 4 4 2 0.74626 0.74626 3 4 4 4 0.59765 0.59765 4 4 4 6 0.46702 0.46702 5 4 4 8 0.35832 0.35832 6 4 4 10 0.27104 0.27104 7 4 4 12 0.20271 0.20271 8 4 4 14 0.15021 0.15021 9 3 5 0 0.90002 0.90002 10 3 5 2 0.67867 0.67867 11 3 5 4 0.47921 0.47921 12 3 5 6 0.32356 0.32356 13 3 5 8 0.21149 0.21149 14 3 5 10 0.13486 0.13486 15 3 5 12 0.08435 0.08435 16 3 5 14 0.05194 0.05194 17 3 5 0 0.97498 0.97498 18 3 5 2 0.89082 0.89082 19 3 5 4 0.78467 0.78467 20 3 5 6 0.67194 0.67194 21 3 5 8 0.56273 0.56273 22 3 5 10 0.46290 0.46290 23 3 5 12 0.37522 0.37522 24 3 5 14 0.30044 0.30044 25 4 5 0 0.89999 0.89999 26 4 5 2 0.72320 0.72320 27 4 5 4 0.55225 0.55225 28 4 5 6 0.40659 0.40659 29 4 5 8 0.29126 0.29126 30 4 5 10 0.20424 0.20424 31 4 5 12 0.14080 0.14080 32 4 5 14 0.09572 0.09572 33 4 5 0 0.97501 0.97501 34 4 5 2 0.91154 0.91154 35 4 5 4 0.83026 0.83026 36 4 5 6 0.74043 0.74043 37 4 5 8 0.64901 0.64901 38 4 5 10 0.56079 0.56079 39 4 5 12 0.47877 0.47877 40 4 5 14 0.40458 0.40458 41 3 6 0 0.90007 0.90007 42 3 6 2 0.65865 0.65865 43 3 6 4 0.44397 0.44397 44 3 6 6 0.28291 0.28291 45 3 6 8 0.17306 0.17306 46 3 6 10 0.10261 0.10261 47 3 6 12 0.05936 0.05936 48 3 6 14 0.03367 0.03367 49 3 6 0 0.97501 0.97501 50 3 6 2 0.87762 0.87762 51 3 6 4 0.75158 0.75158 52 3 6 6 0.61912 0.61912 53 3 6 8 0.49455 0.49455 54 3 6 10 0.38536 0.38536 55 3 6 12 0.29424 0.29424 some non-central F probabilities 2 16:56 Tuesday, March 25, 2008 Obs ndf ddf phi p1 p2 56 3 6 14 0.22090 0.22090 57 4 6 0 0.89996 0.89996 58 4 6 2 0.70491 0.70491 59 4 6 4 0.51722 0.51722 60 4 6 6 0.36211 0.36211 61 4 6 8 0.24471 0.24471 62 4 6 10 0.16089 0.16089 63 4 6 12 0.10347 0.10347 64 4 6 14 0.06535 0.06535 65 4 6 0 0.97503 0.97503 66 4 6 2 0.90101 0.90101 67 4 6 4 0.80298 0.80298 68 4 6 6 0.69463 0.69463 69 4 6 8 0.58636 0.58636 70 4 6 10 0.48500 0.48500 71 4 6 12 0.39437 0.39437 72 4 6 14 0.31607 0.31607 73 6 10 0 0.95012 0.95012 74 6 10 2 0.83318 0.83318 75 6 10 4 0.68729 0.68729 76 6 10 6 0.53880 0.53880 77 6 10 8 0.40493 0.40493 78 6 10 10 0.29378 0.29378 79 6 10 12 0.20690 0.20690 80 6 10 14 0.14207 0.14207