I know...
I've tried to do all the job without external plugins, in the end the penultimate version of the Meta Numerics library is the best solution

Here I've uploaded the manual of that plugin, if there is some useful function to implement let me know and I'l try to add it ASAP...

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

PLUGIN UPDATED SMath Studio 0.97.5737

• added Bessel, BesselJ, BesselY from Meta.Numerics;

If they works correctly and you want I can add also ModifiedBessel and SphericalBessel;

---

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

_______________________________________

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]

______________________________________

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.

What a mess that forum [no accusation]
Last night I added Bessel from source, Nobody replied or acknowledged,,, don't care.
____________________________________

Now, I can see my reply to "Stat Fnct's", superb piece of work. Just something
I don't like, in Scientific/engineering maths, any piece of work must be explicit,
in this "Plugin", fine, necessary functions are included. But whre I bloody hate Smath
is again about the derivative operator ,,, zap: none work. That is above my understanding.

I noticed all sorts of gadgets in the wish list but the essential like the derivative
operator work or do more than derivative of sin(x), absent in the wish list.
Next hyperpriority is the 64 bit floating.

The other complain about this forum is that it has no search engine,
Example: if you search "polylog" ,,, zap, nothing
Google , "Smath, polylog" = zap less than nothing.

Be all good, Jean

Hello Jean,

Wrote

What a mess that forum [no accusation]
Last night I added Bessel from source, Nobody replied or acknowledged,,, don't care.
____________________________________

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

Wrote

....But whre I bloody hate Smath
is again about the derivative operator ,,, zap: none work. That is above my understanding.

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.

Wrote

The other complain about this forum is that it has no search engine,
Example: if you search "polylog" ,,, zap, nothing
Google , "Smath, polylog" = zap less than nothing.

Search engine is not ideal, but it can be helpful
[albumimg]1386[/albumimg]

Regards,
Radovan

Wrote

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

this isn't possible... probably they're from some other plugin (Maple, Maxima, ...)

Quote

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 ...

You're right, most of them are missing (as well as the random generators that are useful too). Where it is possible I'll add them.

Wrote

What a mess that forum [no accusation]

Some mechanisms are still mysterious also for me... :d

Wrote

in this "Plugin", fine, necessary functions are included. But whre I bloody hate Smath
is again about the derivative operator ,,, zap: none work. That is above my understanding.

I noticed all sorts of gadgets in the wish list but the essential like the derivative
operator work or do more than derivative of sin(x), absent in the wish list.
Next hyperpriority is the 64 bit floating.

Andrey has worked and he is working to some keystones, I hope this will let him in a reasonable soon future to improve derivative & integrals.

PLUGIN UPDATED SMath Studio 0.97.5737 and later

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

PLUGIN UPDATED SMath Studio 0.98.6179 and later

• [SS-2422] fixed issues with undefined arguments;
  
• Weibull.pdf - fixed "blue worksheet crash" with shape factor < 1

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

forgot the references...
Multiplicative method for binomial coefficients:
https://en.wikipedia.org/wiki/Binomial_coefficient#Multiplicative_formula


An all around better method would be detailed here (as is a full multiplicative method for calculating the PDF):
http://octave.1599824.n4.nabble.com/attachment/3829107/0/loader2000Fast.pdf

Wrote

An all around better method would be detailed here (as is a full multiplicative method for calculating the PDF):
http://octave.1599824.n4...107/0/loader2000Fast.pdf

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

... do you have a real application for n> 170.

Thank you both, I'll check it ASAP


(messages moved in the appropriate thread)

Wrote

Thank you both, I'll check it ASAP

Maybe like this above 170 ... ?

Stat Treasury_6 Dbin Multiplicative.sm (13 KiB) downloaded 56 time(s).

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/blog/the-statistical-mentor/how-many-samples-do-you-need-to-be-confident-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

Wrote

The application that I'm currently working on involves attribute testing ...

I read you carefully. As it looks, you are confusing yourself
Testing is essentially an Hypergeometric distribution.
Let me check what I have ... not from "dark ages" Minitab.

Jean

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/div898/handbook/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.

Wrote

I don't see the hypergeometric distribution in the source for this plug-in

Here is AOQ, ATI from Hypergeometric just installed an as function.
No need for a plugin for that, just a function.

Stat Hypergeometric [A_T_I].sm (41 KiB) downloaded 59 time(s).
Stat Hypergeometric.sm (77 KiB) downloaded 69 time(s).
Stat Hypergeometric Edu. Copy.sm (62 KiB) downloaded 62 time(s).

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