Thank you Davide for your efforts

I just wish you to implement all the tings for which you have good will and spare time

You know that I am always in favor of Numerical ans Statistical functions implementation in SMath.

To be honest, the things are moving forward much slower that I would like to regarding SMath. Anyway, we just have to accept that.

Best Regards,
Radovan

Just hope that the inverse cumulative distributions would be applied as well. [Radovan]

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Not that many have "inverse cumulative" [quantile] ... easy to check: Maple solve.

Very intersting package, but they are all native in my Smath version [April 2015]

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Quite a few PDF are missing from a very quick check [my Mathcad 11 repository].
I may confuse myself with some of the ones in the package plugin.

Moyal, Weibull_3, Laplace, Hypergeometric, Gamma-Gamma [requires Bessel K],
Gumbel, Fréchet, Dbeta, F[Anova], Gamma, Logistic, Dnbinom, DnormConvolution,
Student 't', Lorentz, Voigt, Kaiser, InvPoly, Assymetric_2sigma ...

As well as quantile, many PDF don't have analytical CDF from symbolic integration.

Cheers, Jean.

Hello Jean,

I could see lots of downloads of your posted files. People are very interested indeed


It was actually mentioned many times that derivative operator is not working quite well.
There are lots of complaints from users - which is Ok. For example search the user Martin Kraska and his posts. You will find very constructive suggestions for improving SMath.


Search engine is not ideal, but it can be helpful


Regards,
Radovan

PLUGIN UPDATED SMath Studio 0.97.5737 and later

- Ceil() and Floor() improved [now with support of units, imaginary numbers, nested matrices/systems];

Davide,

Thank you very much for this plug-in. I have a couple of comments.

The CDF for the binomial distribution returns 0 for 0 successes when it should return the same value as the PDF with 0 successes.

The formula that you are using to calculate the PDF uses factorials:
[f(x,n,p):{n!}/{(x!)*((n-x)!)}*p^x*(1-p)^{n-x}]
This limits the value of the number of trial to less than 170 or an overflow occurs (which SMath catches). A better way may be to use the multiplicative formula to calculate the binomial coefficent term of the PDF which won't overflow until 980 and only then when x = n/2. As x tends away from n/2, the number of trials entered can be significantly increased without overflow. In this case, you need to add the condition that if x = 0 then the binomial coefficient = 1 due to a div/0.

Since the CDF just sums over the PDF as x goes from 0 to x, the same issue exists there as well.

None of this is very robust, but it should make the binomial functions a bit more usable.

Thank you,
Christopher Battles

1. limit 170 => confirmed
2. try to propram "multiplicative"
3. OBSERVE: CDF ... 1-CDF

Thank you both, I'll check it ASAP


(messages moved in the appropriate thread)

Edited by user 06 May 2018 19:59:12(UTC)  | Reason: Not specified

The application that I'm currently working on involves attribute testing and the calculation of confidence and probability of a certain number of events occurring in a set of samples. For example, if there are zero events in 299 trials, then we have 95% confidence that there is a 99% probability that the outcome will not occur.

Some information here from Minitab blog:
http://blog.minitab.com/...ent-your-product-is-good

Very useful in product design testing. And depending on the risk involved, we may need to test to higher confidence levels than that, which leads to higher sample sizes, and therefore higher numbers of trials in the binomial distribution.


Christopher Battles

I agree, the hypergeometric distribution is correct given a finite population. But in this case we assume an infinite (or very large) population that we sample from. Therefore the probability does not change due to the sampling. An assumption, yes, but one that is accepted for large populations.

https://www.itl.nist.gov.../pmc/section2/pmc232.htm

I don't see the hypergeometric distribution in the source for this plug-in, but the same overflow issue will arise with that calculation as well since it requires calculating the binomial coefficients. So n! will raise it's ugly head again.

Jean,
Very nice workbooks. I'll have to study them a bit.
Thank you very much!
Chris