(35S) Statistical Distributions Functions

[Dieter]

(10-27-2015 07:32 PM)Dieter Wrote:  BTW, at the moment I am looking at an 35s implementation of the HP67 routines.

OK, here is a first experimental version of the Chi² algorithm used in the HP67 Stat Pac. PDF and CDF are calculated simultaneously, and both are returned in Y and X. Here is the code:

Code:

C001  LBL C
C002  INPUT J
C003  e
C004  IP
C005  STO T
C006  ÷
C007  !
C008  STO G
C009  INPUT X
C010  XEQ C013
C011  STOP
C012  GTO C009
C013  RCL X
C014  RCL÷ T
C015  +/-
C016  e^x
C017  LASTx
C018  +/-
C019  RCL J
C020  RCL÷ T
C021  y^x
C022  x
C023  RCL÷ G
C024  STO A
C025  RCL J
C026  STO B
C027  SGN
C028  ENTER
C029  -
C030  ENTER
C031  ENTER
C032  LASTx
C033  RCLx X
C034  RCL B
C035  RCL+ T
C036  STO B
C037  ÷
C038  +
C039  x≠y?
C040  GTO C030
C041  RCL A
C042  RCL X
C043  x=0?
C044  e^x
C045  ÷
C046  RCLx J
C047  RCL÷ T
C048  x<>y
C049  RCLx A
C050  RCL+ A
C051  RTN

Usage (results as shown in FIX 9 mode):

Code:

[XEQ] C [ENTER]             J=?

Enter degrees of freedom
    10  [R/S]               X=?

Enter random variable X
    6,3 [R/S]               0,087896860   // =PDF(6,3|10)
                            0,210539719   // =CDF(6,3|10)
Do another calculation
        [R/S]               X=?
    20  [R/S]               0,009458319   // =PDF(20|10)
                            0,970747312   // =CDF(20|10)

As usual, comments, suggestions and error reports are welcome. ;-)

Since the main computation routine (C013 ff.) returns both the PDF and the CDF, adding a function that determines the inverse (quantile) is rather simple. I tried an approach using a second-order (Halley) method and it worked well for me. This required about 30 additional lines of code.

Dieter