A previous article shows how to use a recursive formula to compute exact probabilities for the Poisson-binomial distribution. The recursive formula is an O(N2) computation, where N is the number of parameters for the Poisson-binomial (PB) distribution. If you have a distribution that has hundreds (or even thousands) of parameters,
When working with a probability distribution, it is useful to know how to compute four essential quantities: a random sample, the density function, the cumulative distribution function (CDF), and quantiles. I recently discussed the Poisson-binomial distribution and showed how to generate a random sample. This article shows how to compute
The Poisson-binomial distribution is a generalization of the binomial distribution. For the binomial distribution, you carry out N independent and identical Bernoulli trials. Each trial has a probability, p, of success. The total number of successes, which can be between 0 and N, is a binomial random variable. The distribution
Many textbooks and research papers present formulas that involve recurrence relations. Familiar examples include: The factorial function: Set Fact(0)=1 and define Fact(n) = n*Fact(n-1) for n > 0. The Fibonacci numbers: Set Fib(0)=1 and Fib(1)=1 and define Fib(n) = Fib(n-1) + Fib(n-2) for n > 1. The binomial coefficients (combinations
A previous article discussed how to solve regression problems in which the parameters are constrained to be a specified constant (such as B1 = 1) or are restricted to obey a linear equation such as B4 = –2*B2. In SAS, you can use the RESTRICT statement in PROC REG to
Matrix balancing is an interesting problem that has a long history. Matrix balancing refers to adjusting the cells of a frequency table to match known values of the row and column sums. One of the early algorithms for matrix balancing is known as the RAS algorithm, but it is also
On discussion forums, many SAS programmers ask about the best way to generate dummy variables for categorical variables. Well-meaning responders offer all sorts of advice, including writing your own DATA step program, sometimes mixed with macro programming. This article shows that the simplest and easiest way to generate dummy variables
Have you ever seen the "brain teaser" for children that shows a 4 x 4 grid and asks "how many squares of any size are in this grid?" To solve this problem, the reader must recognize that there are sixteen 1 x 1 squares, nine 2 x 2 squares, four 3 x 3 squares, and one 4 x 4 square.
When you write a program that simulates data from a statistical model, you should always check that the simulation code is correct. One way to do this is to generate a large simulated sample, estimate the parameters in the simulated data, and make sure that the estimates are close to
Last month a SAS programmer asked how to fit a multivariate Gaussian mixture model in SAS. For univariate data, you can use the FMM Procedure, which fits a large variety of finite mixture models. If your company is using SAS Viya, you can use the MBC or GMM procedures, which
