MaplePrimes - answers and comments on Question, Animated Standard Normal Distribution

Two animations

Kitonum — Sun, 23 Dec 2012 13:07:58 Z

Change in the normal curve phi(x)=1/(sigma*sqrt(2*Pi))*exp(-(x-a)^2/(2*sigma^2)) as the parameter a is changing from -2 to 3 (sigma=1) :

plots[animate](plot,[1/sqrt(2*Pi)*exp(-(x-a)^2/2),x=-5..6,thickness=2],a=[seq(-2+0.02*k,k=0..250)]);

Change in the normal curve phi(x)=1/(sigma*sqrt(2*Pi))*exp(-(x-a)^2/(2*sigma^2)) as the parameter sigma is changing from 0.6 to 2 (a=1) :

plots[animate](plot,[1/sigma/sqrt(2*Pi)*exp(-(x-2)^2/2/sigma^2),x=-2..6,thickness=3],sigma=[ seq(0.6+k*0.005,k=0..280)]);

Another way

Markiyan Hirnyk — Sun, 23 Dec 2012 13:27:57 Z

In order to satisfy the questioner, one may consider a plot with range x=-infinity..infinity and the use of the Explore command

Explore(plot(exp(-(1/2)*((x-a)/sigma)^2)/sqrt(2*Pi*sigma^2), x = -infinity .. infinity))

PS. The sigma range may be 0.001..10. and the range for the parameter a may be put -10. .. 10. . Pay attention to the decimal points in the ranges. It makes a smoother animation.

a little more general

PatrickT — Sun, 23 Dec 2012 23:07:44 Z

Based on Kitonum's code, but using the built-in PDF for the Normal distribution. The advantage is that you can easily adapt the code to another distribution, if you were so inclined, and you don't have to remember the PDF of the distribution, and you avoid possible mis-typing of the distribution.

Side remark: I did not detect any advantage in terms of speed or memory usage

CodeTools:-Usage(# based on Kitonum
plots:-animate(plot, [Statistics:-PDF(Statistics:-RandomVariable(Normal(mu,1)),x), x=-5..6,'thickness'=2,'color'=blue], mu=[seq(-2+0.02*k,k=0..250)])
);

For fun, here an animation as the "entropy" H varies between 0 and 1.

h := 1/2*ln(2*Pi*exp(1)*sigma^2);
sig := solve(H=h,sigma,UseAssumptions) assuming sigma>0;
pdfN := Statistics:-PDF(Statistics:-RandomVariable(Normal(mu,sigma)),x):
pdfNs := unapply( eval(pdfN,sigma=sig), (mu,H) ):
plots:-animate( plot, [pdfNs(0,H), x=-5..5,'thickness'=2,'color'=blue], H=[seq(i,i=0..1,0.01)] );

Where's my original animation?

Douglas Lewit — Mon, 24 Dec 2012 17:58:41 Z

minor edit

PatrickT — Sun, 23 Dec 2012 23:15:17 Z

you can write seq more simply, like this instead: H=[seq(0..1,0.01)]