518 – Software for Statistical Computing
Turning the Tables on Probability Distributions
Stephen M. Mansour
Kania School of Management, University of Scranton
While software has replaced the need for tables in statistics courses, many statistical programs do not go far enough. Some programs have several separate functions for each distribution, and some only calculate cumulative probabilities. Ideally, a software program should have exactly one function per distribution. Combining this distribution function with a relation allows us to calculate a whole host of probabilities consistently. The secret is in the use of operators which modify functions or combine two functions to produce another function. While operators may seem esoteric to many, the resulting syntax appears surprisingly English-like. For example, to find the probability that a randomly-selected student is taller than 6 feet, given a normal distribution with mean and standard deviation of 68 and 3 inches respectively, we simply state: 68 3 normal probability > 72 which produces a value of 0.09121. This syntax is easily implemented in a functional programming language such as APL.