By B.V. Cordingley, D.J. Chamund

ISBN-10: 0333435699

ISBN-13: 9780333435694

ISBN-10: 1349092827

ISBN-13: 9781349092826

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Requires subroutines LNGAMM and GAMMFN. Method The distribution function for chi-squared is Fx(x) = (1/(2 m/2 rctm))) F x(x) = 0 x <0 f: u(m-2)/2 exp(-u/2) du x;;;;t 0 m = 1, 2 ... where m is the number of degrees of freedom. This may be treated as a special case of the incomplete gamma distribution: G(y,p) =(l/r(p)) f: tp-1exp(-t) dt p > O,y > 0 in which 2p = m and 2y = x. The subroutine employs this relationship to evaluate F x(x). Subroutine Listing 4000 4010 4020 4030 4040 4050 4060 4070 4080 4090 4100 4110 4120 4130 4140 4150 4160 4170 4180 4190 REM REM REM REM REM REM REM REM REM REM REM REM REM REM REM REM REM CHI-SQUARED DISTRIBUTION FUNCTION SUBROUTINE: CHISQD COMPUTES AREA UNDER CHI-SQUARED DISTRIBUTION FOR OF DEGREES OF FREEDOM FROM ZERO TO XCHI REQUIRES SUBROUTINES GAMMFN AND LNGAMM VARIABLES: INPUT: DF ......

84. 24. 30. 47. 8. 1. 5982 DATA 8. 4. 0. 8. 4. 8 PRINT HEADINGS. READ DATA. COMPUTE FAREA CALL SUBROUTINE FDISTR FOR EACH SET OF DATA PRINT" D1o'l". " XF"; PRINT " FAREA" LET N1 = 8 FOR I = 1 TO N1 READ DF1. DF2. XF GOSUB 4000 PRINT DF1. DF2. XF. 97E-3 1E-2 1E-3 1E-2 The results agree with those published in tables of the upper percentage points of the F-distribution. The Subroutines 47 UPPER TAIL OF STUDENT'S T DISTRIBUTION Subroutine: TDISTR Description Computes the area under the upper tail of Student's central t distribution for n degrees of freedom.

Method The distribution function for chi-squared is Fx(x) = (1/(2 m/2 rctm))) F x(x) = 0 x <0 f: u(m-2)/2 exp(-u/2) du x;;;;t 0 m = 1, 2 ... where m is the number of degrees of freedom. This may be treated as a special case of the incomplete gamma distribution: G(y,p) =(l/r(p)) f: tp-1exp(-t) dt p > O,y > 0 in which 2p = m and 2y = x. The subroutine employs this relationship to evaluate F x(x). Subroutine Listing 4000 4010 4020 4030 4040 4050 4060 4070 4080 4090 4100 4110 4120 4130 4140 4150 4160 4170 4180 4190 REM REM REM REM REM REM REM REM REM REM REM REM REM REM REM REM REM CHI-SQUARED DISTRIBUTION FUNCTION SUBROUTINE: CHISQD COMPUTES AREA UNDER CHI-SQUARED DISTRIBUTION FOR OF DEGREES OF FREEDOM FROM ZERO TO XCHI REQUIRES SUBROUTINES GAMMFN AND LNGAMM VARIABLES: INPUT: DF ......

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Advanced BASIC Scientific Subroutines by B.V. Cordingley, D.J. Chamund


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