Tooltips and improvements to the calculator probability keyboard

[rdstern]

Here is the second keyboard for the tooltips. At the same time I suggest some improvements and the correction of an error.

1. The errors first. In the existing keyboard the pF key actually delivers the pchisq function. Correct this to give pf. And the pchi key gives pt! So change that to give pchisq. Then change pF and qF keys to pf and qf (which corresponds to the function names.)
2. There are currently 18 keys in the keyboard, but they are not in logical and clear positions. I propose an improved layout together with the addition of 12 more keys. So there will be a 5 by 6 array of keys. As follows:

Row 1: pnorm, pt, pchisq, pF, pgamma Row 2: qnorm, qt, qchisq, qF, qgamma Row 3: pbeta, pbirth, pbinom, ppois, pnbin Row 4: qbeta, qbirth, qbinom, qpois, qnbin Row 5: fact, choose, beta, gamma, digamma Row 6: lfact, lchoose, lbeta, lgamma, trigamma

Note, if need be, then some of the keys can be shortened to fit, e.g. pbin could be instead of pbinom.

The distrbutions are all described in this page. For example pbirth is the birthday problem, function pbirthday and qbirthday. That distribution is a useful idea in teaching.

Next the tooltips for these keys.

[rdstern]

Suggested tooltips for new keyboard: pnorm: normal probabilities. For example: pnorm(-1.6449) = 0.05; pnorm(130,100,15) = 0.9772. pt: t probabilities. For example pt(-2,5) = 0.051; pt(-2,1000) = 0.0229 ~ pnorm(-2) pchisq: chi square probabilities. For example pchisq(5,1) = 0.9747; pchisq(5,10) = 0.1088 pf: F probabilities. For example pf(2,1,10) = 0.8123; pf(2,50,50) = 0.9921 pgamma gamma probabilities. For example pgamma(2,1,1) = 0.8647; (Exponential) pgamma(2,10,10) = 0.995 qnorm: normal quantiles. For example qnorm(0.05) = -1.6449; qnorm(0.9772, 100,15) = 130 qt: t quantiles. For example qt(0.05, 5) = -2.015; qt(0.05, 100) = -1.66 qchisq chi square quantiles. For example qchisq(0.95, 1) = 3.841; qchisq(0.95, 10) = 18.31 qf F quantiles. For example qf(0.95,1,10) = 4.965; qf(0.95, 50,50)= 1.599 qgamma gamma quantiles. For example qgamma(0.95,1,1) = 2.995; qgamma( 0.95,10,10) = 1.571 pbeta beta probabilities. For example pbeta(0.8,1,1) = 0.8 (Uniform); pbeta(0.8,10,10) = 0.9984 qbeta beta quantiles. For example qbeta(0.2,1,1) = 0.2 (Uniform); qbeta(0.95,10,10) = 0.6799 More to come

[rdstern]

pbirth: simultaneous birthday probabilities. For example pbirthday(10) = 0.1169 ; pbirthday(50) = 0.97 qbirth: simultaneous birthday quantiles. For example qbirthday(0.5) = 23, qbirthday(0.99) = 57 pbinom: binomial probabilities. For example pbinom(3,5,0.4) = 0.0.913 qbinom: binomial quantiles. For example qbinom(0.9,5,0.4) = 3 ppois: Poisson probabilities. For example ppois(8, 5) = 0.93 qpois:Poisson quantiles. For example qpois(0.9, 5) = 8 pnbinom: negative binomial probabilities. For example pnbinom(4,1,0.4) = 0.922 (geometric); pnbinom(13,5,0.4) = 0.9058 qnbinom: negative binomial quantiles. Fro example qnbinom(0.9,1,0.4) = 4 (geometric); qnbinom(0.9, 5,0.4) = 13

[rdstern]

factorial: factorial. For example factorial(4) = 4321 = 24; factorial(3.5) = gamma(4.5) = 11.63 lfactorial: log factorial. For example lfactorial(400) = 2001 choose: binomial coefficient. For example choose(7,4) = 7!/(4!3!) = 35 lchoose: log binomial coefficient. For example lchoose(700,400) = 474.5 beta: beta function. For example beta(6,2) = gamma(6)gamma(2)/gamma(8) = 0.02381 lbeta: log beta function. For example lbeta(100,40) = -84.51 gamma: gamma function. For example gamma(8) = fact(7) = 5040 lgamma: log gamma function. For example lgamma(800) = 4545 digamma: digamma function. For example digamma(1) = -0.5772 (Euler's constant) trigamma: trigamma function. For example trigamma(1) = 1.645 (pipi/6)

And please check the summary keyboard on your branch. It seems to have been displaced.