Calculators with normal distribution and inverse?

[Dave Britten]

Which HP calculators have built in functions for calculating a standard normal probability distribution - probability for a given upper/lower tail - as well as its inverse? So far I've only seen this on the 21S, 10bII+, and possibly the 20b/30b. Were there any others that included this?

[Maximilian Hohmann]

Hello!

(09-09-2020 06:15 PM)Dave Britten Wrote:  Were there any others that included this?

Other calculators from HP or from different manufacturers? The Ti-89/200 Voyage for example has a built-in function called "invnorm". Not that I have the least idea what purpose this can serve in real life.

Regards
Max

[Dave Britten]

(09-09-2020 06:32 PM)Maximilian Hohmann Wrote:  Hello!

(09-09-2020 06:15 PM)Dave Britten Wrote:  Were there any others that included this?

Other calculators from HP or from different manufacturers? The Ti-89/200 Voyage for example has a built-in function called "invnorm". Not that I have the least idea what purpose this can serve in real life.

Regards
Max

I'm primarily interested in HPs, though I'd be interested in hearing about about other manufacturers too. I know most relatively recent Casio graphing calculators have these functions, though I can't say for sure when they started including them. Probably around the fx-9750G, if I had to guess. I think the same goes for all varieties of TI-83/84, the TI-82 Stats, and probably the Nspire line. And older models like the TI-36 Solar (not the TI-36X Solar) and maybe TI-35 Plus have it.

One useful application of the inverse normal function is obtaining a Z-score for a given confidence level and using that to compute a minimum sample size for a given confidence interval and population size.

Example: https://www.surveysystem.com/sscalc.htm

[Gene]

The original HP-27 had these functions, but it is a bit difficult to find. :-)

[Dave Britten]

(09-09-2020 07:15 PM)Gene Wrote:  The original HP-27 had these functions, but it is a bit difficult to find. :-)

Oh yeah, you're right! Though it doesn't have the inverse (P->Z), just the usual upper-tail Q(x). Still cool though.

[KeithB]

I am pretty sure the Prime has it - even different distributions, IIRC.

[John Keith]

The 48g/49/50 have UTPN (upper tail probability) and NDIST (normal distribution at x). No inverse AFAIK. Lower tail probability is easily computed from upper.

Here is a long thread on computing the normal distribution.

[Etienne Victoria]

Also the Hp-32E.

https://www.hpmuseum.org/cgi-bin/compare...e&shade=ON

[Gene]

32E - which has Q and Q-1.

[Mike T.]

The HP32E implemented both Q and Q-1 which I think are what you are looking for. It could take its time to evaluate the latter, but it was way quicker than using the normal distribution tables and wonderful to watch!

If those functions are available on my later HP32S, then I'd agree that they very are hard to find!

[peacecalc]

Hello all,

here is the link to short programs calculating the inverse of the build in distributions:
https://www.hpmuseum.org/forum/thread-2431.html

The invers is useful i. e. for getting an answer about confidental interval.

[Dave Britten]

Demosthenes kindly reminded me that the WP-34S and WP-31S have a boatload of stat distribution functions, the normal distribution among them.

Are there any interesting non-graphing Casios I've overlooked? The fx-5800P has P(x), Q(x), and R(x), but it doesn't seem possible to calculate inverses. I tried solving P(X)=Y but it just gave a syntax error.

[ijabbott]

(09-14-2020 07:32 PM)Dave Britten Wrote:  Are there any interesting non-graphing Casios I've overlooked? The fx-5800P has P(x), Q(x), and R(x), but it doesn't seem possible to calculate inverses. I tried solving P(X)=Y but it just gave a syntax error.

The Casio fx-115/570/991 ES Plus and EX ranges can calculate Normal PD, Normal CD and Inverse Normal CD (as well as Binomial PD, Binomial CD, Poisson PD, and Poisson CD) distributions.

[rawi]

(09-09-2020 06:15 PM)Dave Britten Wrote:  Were there any others that included this?

Other calculators from HP or from different manufacturers? The Ti-89/200 Voyage for example has a built-in function called "invnorm". Not that I have the least idea what purpose this can serve in real life.
[/quote]

The TI-Nspire CAS has the inverse of the Normal-distirbution, the t-distribution and the Chi²-distribution.
The inverse distributions are useful as well for simulation problems. If you have equally between 0 and 1 distributed random numbers you can easily generate otherwise distributed random numbers by using the inverse of the cumulated density function.

Best

Raimund