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Abstract:
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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 (e.g. >, < or between) allows us to calculate a whole host of probabilities consistently. The secret is in the use of operators, which modify functions, or which combine two functions to produce a new function. While operators may seem somewhat esoteric, 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, one simply states: "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. The concept can be extended to finding critical values, generating random variables for simulation, and determining theoretical values.
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