'****************************************************
'* Program to demonstrate the chi-square subroutine *
'* ------------------------------------------------ *
'* Reference: BASIC Scientific Subroutines, Vol. II *
'* By F.R. Ruckdeschel, BYTE/McGRAWW-HILL, 1981 [1].*
'* ------------------------------------------------ *
'* SAMPLE RUN:                                      *
'* How many degrees of freedom: 100                 *
'* What is the range (X1,X2):                       *
'*   X1: 50                                         *
'*   X2: 150                                        *
'* What is the table step size: 5                   *
'*                                                  *
'*    X       Chi-Square PDF                        *
'*   ------------------------                       *
'*    50        0.00000                             *
'*    55        0.00003                             *
'*    60        0.00018                             *
'*    65        0.00076                             *
'*    70        0.00237                             *
'*    75        0.00571                             *
'*    80        0.01107                             *
'*    85        0.01772                             *
'*    90        0.02393                             *
'*    95        0.02779                             *
'*   100        0.02816                             *
'*   105        0.02525                             *
'*   110        0.02025                             *
'*   115        0.01468                             *
'*   120        0.00970                             *
'*   125        0.00588                             *
'*   130        0.00330                             *
'*   135        0.00172                             *
'*   140        0.00084                             *
'*   145        0.00038                             *
'*   150        0.00017                             *
'*                                                  *
'****************************************************
DEFINT I-N
DEFDBL A-H, O-Z
CLS
PRINT
INPUT " How many degrees of freedom: ", m
PRINT " What is the range (X1,X2):"
INPUT "   X1: ", x1
INPUT "   X2: ", x2
INPUT " What is the table step size: ", x3
CLS
PRINT
PRINT "   X       Chi-Square PDF "
PRINT " -------------------------"
FOR x = x1 TO x2 STEP x3
  GOSUB 2000
  PRINT USING "  ###        #.#####"; x; y
NEXT
END

'***************************************************
'* Series approximation subroutine LN(X!)          *
'* Accuracy better then 6 places for x>=3          *
'* Accuracy better than 12 places for x>10         *
'* Advantage is that very large values of the      *
'* argument can be used without fear of over flow. *
'* x is the input, y is the output.                *
'* ----------------------------------------------- *
'* Reference: CRC Math Tables.                     *
'***************************************************
1000 x1 = 1# / (x * x)
  y = (x + .5#) * LOG(x) - x * (1# - x1 / 12# + x1 * x1 / 360# - x1 * x1 * x1 / 1260# + x1 * x1 * x1 * x1 / 1680#)
  y = y + .918938533205#
RETURN

'******************************************************
'* Chi-square function subroutine. This program takes *
'* a given degree of freedom, m and value, x, and     *
'* calculates the chi-square density distribution     *
'* function value, y.                                 *
'* -------------------------------------------------- *
'* Reference: Texas Instruments SR-51 owners Manual,  *
'* 1974.                                              *
'* -------------------------------------------------- *
'* Subroutine used: LN(X!).                           *
'******************************************************
2000 'Save X
  xm1 = x
  'Perform calculation
  x = m / 2 - 1#
  'Call LN(X!) subroutine
  GOSUB 1000
  x = xm1
  c = -x / 2 + (m / 2 - 1) * LOG(x) - (m / 2) * LOG(2) - y
  y = EXP(c)
RETURN

'End of file chi-sqr.bas