cas/xcas implementation of Geometric PDF

05092021, 06:40 PM
Post: #1




cas/xcas implementation of Geometric PDF
I've been wondering about the Geometric PDF/CDF/ICDF functions on the Prime. The syntax for the PDF is:
GEOMETRIC(p,k) which gives the probability of the first success occurring on the kth trial, ie, (1p)^(k1) * p On other implementations that I have seen, the Geometric PDF is a discrete PDF, requiring k to be a natural number. While the xcas help screen indicates that k is an integer, both xcas and Prime cas allow k to have any positive decimal value. In essence, this makes Geometric a continuous distribution. My question is whether this was intentional? And if so, what would be an example application of using the Geometry PDF in such a continuous manner? Does a continuous Geometric PDF have a physical meaning? The CDF version likewise allows decimals for k, applied to the usual 1(1p)^k. One sideeffect of this is that the behavior differs from other continuous pdf's in that the cdf is no longer the area under the pdf curve. chisquare_cdf(12,10) = ∫(chisquare(12,x),x,0,10) but GEOMETRIC_CDF(0.3,4) ≠ ∫(GEOMETRIC(0.3,x),x,0,4) From this it would seem that the Geometric CDF/PDF's are really intended to be discrete. Usually on discrete inverse functions, the returned value can only be a whole number, but no such rounding is done with GEOMETRIC_ICDF(), like a continuous function. So the implementation has characteristics of both discrete and continuous pdf's. Maybe someone can shed some light on this. 

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Messages In This Thread 
cas/xcas implementation of Geometric PDF  Wes Loewer  05092021 06:40 PM
RE: cas/xcas implementation of Geometric PDF  parisse  05102021, 06:23 PM
RE: cas/xcas implementation of Geometric PDF  Wes Loewer  05122021, 06:37 PM

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