(35S) Statistical Distributions Functions

[Dieter]

(11-20-2015 01:19 PM)Dieter Wrote:  BTW, it seems that the program titled "Distribución Polinomial" actually calculates the multinomial distribution (es: distribución multinomial). Since I am not sure about the correct Spanish term: is there a difference between these two expressions or do they refer to the same distribution? If yes: the multinomial distribution can be calculated much easier and without using so many registers.

OK, here is a version that features some advantages:

• Usage is quite straightforward. No need to prestore values in registers or calculate sums manually.
• Uses merely two registers instead of eleven.
• Number k of events can be anything between 1 and ...infinity
• Erroneous data entry can be corrected by re-entering with a negative frequency x.
• Despite all this: shorter. Could be even shorter (not much more than 20 lines) without the error recovery function (see below)
  

Here is the listing:

Code:

M001  LBL M
M002  CLSTK
M003  STO N     n=0
M004  e^x
M005  STO P     p=1
M006  ALL
M007  CLSTK
M008  VIEW N    show accumulated n
M009  x=0?      zero or no entry?
M010  GTO M027  jump to probability calculation
M011  x<>y
M012  STO+ N    n := n + x_i
M013  SGN
M014  x<>y      save sign(x_i)
M015  LASTx
M016  ABS
M017  y^x
M018  LASTx
M019  !
M020  ÷         p_i^x_i / x_i!
M021  x<>y      if xi was negative this is -1 (instead of 1 else)
M022  y^x       which turns this into its reciprocal
M023  STOx P    update product
M024  GTO M006
M025  RCL N
M026  !
M027  STOx P    calculate probability
M028  FIX 6
M029  RCL P     return result in X
M030  VIEW P    and display labelled output
M031  GTO M001  start a new calculation with R/S

Here is an example using the data from your (Pedro's) PDF:

Code:

 x1 = 2     p1 = 0,25
 x2 = 2     p2 = 0,25
 x3 = 5     p3 = 0,25
 x4 = 3     p4 = 0,25


 [XEQ] M  [ENTER]
                       N=         0    // Data is entered by
 2 [ENTER] 0,25 [R/S]                  // x_i [ENTER] p_i  [R/S]
                       N=         2
 2 [ENTER] 0,25 [R/S]
                       N=         4
 5 [ENTER] 0,5  [R/S]
                       N=         9    // oops... wrong data
-5 [ENTER] 0,5  [R/S]                  // re-enter with negative x
                       N=         4    // and it gets removed
 5 [ENTER] 0,25 [R/S]
                       N=         9
 3 [ENTER] 0,25 [R/S]
                       N=        12
                [R/S]                  // data complete, simply press [R/S] or 0 [R/S]
                       P=  0,009913    // result

Hmmm... I just got another idea. Maybe this could be done with the Σ+ key using a sum of logs instead of a product... *8)

Edit: Yes, this will also work:

Code:

M001  LBL M
M002  CLΣ
M003  ALL
M004  Σx
M005  STO N
M006  CLSTK
M007  VIEW N
M008  x=0?
M009  GTO M030
M010  LN
M011  x<>y
M012  SGN
M013  STO N     save sign(x_i)
M014  LASTx     * x_i
M015  x         = abs(x_i)
M016  x
M017  LASTx
M018  ENTER
M019  R↓
M020  !
M021  LN
M022  -
M023  R↑
M024  RCLx N    multiply
M025  x<>y      both values
M026  RCLx N    by +1 or -1
M027  x<>y      so that this
M028  Σ+        Σ+ may become a Σ-
M029  GTO M003
M030  Σx
M031  !
M032  LN
M033  Σy
M034  +
M035  e^x
M036  STO P
M037  FIX 6
M038  VIEW P
M039  GTO M001

Program usage is the same as before. The code uses only logs of the factorial function (both "!" are followed by a "LN") so that this approach may be especially useful for calculators with lnΓ function, thus avoiding potential overflow problems.

Dieter