Sometimes a graph is more interpretable if you assign specific colors to categories. For example, if you are graphing the number of Olympic medals won by various countries at the 2012 London Olympics, you might want to assign the colors gold, silver, and bronze to represent first-, second-, and third-place
The New York Times has an excellent staff that produces visually interesting graphics for the general public. However, because their graphs need to be understood by all Times readers, the staff sometimes creates a complicated infographic when a simpler statistical graph would show the data in a clearer manner. A
Last week I wrote a SAS/IML program that computes the odds of winning the game of craps. I noted that the program remains valid even if the dice are not fair. For convenience, here is a SAS/IML function that computes the probability of winning at craps, given the probability vector
It is easy to simulate data that is uniformly distributed in the unit cube for any dimension. However, it is less obvious how to generate data in the unit simplex. The simplex is the set of points (x1,x2,...,xd) such that Σi xi = 1 and 0 ≤ xi ≤ 1
Gambling games that use dice, such as the game of "craps," are often used to demonstrate the laws of probability. For two dice, the possible rolls and probability of each roll are usually represented by a matrix. Consequently, the SAS/IML language makes it easy to compute the probabilities of various
John D. Cook posted a story about Hardy, Ramanujan, and Euler and discusses a conjecture in number theory from 1937. Cook says, Euler discovered 635,318,657 = 158^4 + 59^4 = 134^4 + 133^4 and that this was the smallest [integer]known to be the sum of two fourth powers in two
Did you know that you can index into SAS/IML matrices by using unique strings that you assign via the MATTRIB statement? The MATTRIB statement associates various attributes to a matrix. Usually, these attributes are only used for printing, but you can also use the ROWNAME= and COLNAME= attributes to subset
I was recently flipping through Ross' Simulation (2006, 4th Edition) and saw the following exercise: Let N be the minimum number of draws from a uniform distribution [until the sum of the variates]exceeds 1. What is the expected value of N? Write a simulation to estimate the expected value. For
Sometimes it is useful to group observations based on the values of some variable. Common schemes for grouping include binning and using quantiles. In the binning approach, a variable is divided into k equal intervals, called bins, and each observation is assigned to a bin. In this scheme, the size
With the US presidential election looming, all eyes are on the Electoral College. In the presidential election, each state gets as many votes in the Electoral College as it has representatives in both congressional houses. (The District of Columbia also gets three electors.) Because every state has two senators, it
