(19C/29C) (k-)Permutations, Combinations, Linear Regression and Pseudo-random number

[Archilog]

Hello Gene,

To briefly answer your question, I already had the idea to write an 'as-complete-as-possible' set of routines in order to study a function (extremum, derivative, integral area, etc.). I think it would be quite challenging...
I also have other ideas more specific, in astronomy for instance.

Now about the distribution: I wrote probably an error saying that the "A(n+1) =frac(997∗A(n))" algorithm is better than the "A(n+1) =frac((π+A(n))^5" algorithm.

I checked this morning the first one in the program, and when I tried to lazily modify the example ("0.5 in X register will generate sequence 0.41, 0.58, 0.45, 0.51, 0.11, 0.26, etc."), to my surprise the sequence became... 0.5, 0.5, 0.5 (ad lib), which is obvious since every odd integer multiplied by 0.5 (or divided by 2) gives a fractional part equaling 0.5.

So I remembered an 'old' article I highly recommend about the subject. Despite some good statistical appearances (see below), a graphical representation of their distribution may show an anormal - or too oriented - result (see picture).

Code:


Seed: 0.123456                         A(n+1) = frac(997∗A(n)) || A(n+1) = frac((π+A(n))^5
MEAN                                      0.50124              ||             0.48313 
VARIANCE                                  0.08247              ||             0.08221
AUTOCORRELATION COEF                      0.24780              ||             0.23630

   

Here is the article I refer to (see page 7). Sorry, it is in French, but I am more French than statistician ;)). However one can find therein good and quick codes in BASIC or for the HP-39GII easy to understand to compare some PRN generators.

I don't know to which PPC articles you refer, be sure I would like to read them, please. I own a DVD of Jake Schwartz if needed.

In conclusion, I didn't modify the last routine. But I am open-minded, I could do so if necessary. :)

Regards!