In this post I'll introduce is a nice visual test of randomness from signal processing. The main idea of this test to look at how a random sequence correlates with itself.

It's been a while since I wrote one of these random posts, but I still have a couple more I wanted to write.  In this post, I want to describe one of the tests used in the paper that initially inspired this series of posts: the Wald-Wolfowitz runs test.  This test is interesting in that it does not test for uniformity

A new edition of Maplets for Calculus  (M4C) is now available.  M4C v1.3 is a collection of 129 maplets for calculus students and instructors.  The 35 new maplets fill in some gaps in the coverage of precalculus and single variable calculus and begin to address multivariate topics. Each maplet provides a customized graphical user interface (using 2D and 3D graphics and animation) to provide immediate, step-by-step guidance through an endless supply of random ...

I would like to pay the attention of the MaplePrimes users
to a Robert Chero application.
This is a Maple package on graphics, which can be implemented in Maple as a usual package.
It  has community rating 4.5 stars. This package can be downloaded from http://www.maplesoft.com/applications/view.aspx?SID=1671.
It was submitted in 2005 when MaplePrimes started. Because of this reason this...

As a user of Maple 13, namely in computations on General Relativity & Tensor Calculus, I would like to let you know I just got, using Maple 13, the WRONG SIGN (positive Riemann scalar curvature in stead of correct NEGATIVE Riemann scalar curvature) in studying a threefold used as a 'Public Space' by Milne many years ago.

The square of the distance on the said threefold is dE^2=dR^2+(c*t0)^2*sinh(R/(c*t0))^2*(dtheta^2+sin(theta)^2*dphi^2) and you might be interested...

As alluded to in my previous post in this series, one of the most straight forward ways to test if a PRNG is generating good random sequences is by examining the frequency of 0's and 1's.  This is just a couple lines in Maple using Statistics:

(**) r1 := rand(0..1):L := [seq(r1(), i=1..10000)]:
(**) n := nops(L); tally := `+`(op(L));
(**) Statistics:-ChiSquareGoodnessOfFitTest(
      [n-tally, tally], [n/2, n/2], ':-output'=':-hypothesis');

I thought for sure something like this would have already been done in Maple (mapleprimes).  I see it's already been done over at Mathematica.  I must admit I am a bit jealous at how much Mathematica users have done.  So anyways ... something simple

for i from 1 to 10 do
  for j from 1 to 10 do

This is the third post in a four-part series; the earlier posts are Generating...

This is the second post in a four-part series that started with this post: Generating...

Maple's Statistics package contains many predefined probability distributions; well-known ones such as the normal distribution and lesser-known ones such as the Gumbel distribution. For these distributions, we ship efficient algorithms that can quickly generate a large number of sample points. To generate a sample of size 10⁶ of both of these distributions, and print the time it took to do this (in seconds), you can run the following:

with(Statistics):

This describes in more detail (with permission and citation) the method posted here of solving problem 2 in the XKCD comic Substitute.

Download RaptorMath.mw

Today is my birthday, and in fact it is also the birthday of at least one other Maplesoft employee (not surprising since more than 23 people work here - considering the generalized birthday problem, I even know of 3 people here who share the same birthday).  Of course, it turns out that birthdays are not evenly distributed through out the year and so I wanted to know if someone with an August birthday is more likely to share than someone with an April birthday. 

Look at this article (Its loading can take a few minutes: approximately 5 MB.). All those pictures could be created with Maple.

PS. Working link to  the article.

Continuing on in this series of posts, here is a way to test the randomness of a sequence of bits from a PRNG that is the appropriate to the first morning back after the August long weekend.  It is a very fast, and not very formal test done by checking how well a sequence compresses. This is really easy in Maple 14, with the new commands ?StringTools:-Compress and StringTools:-Uncompress which use ...