A Taylor's Theorem--Central Limit Theorem Approximation: Its Use in Obtaining the Probability Distribution of Long-Range Profit

Although the functional relationship between long-range profit (LRP) and its various components is usually well defined, the difficulty of determining the probability distribution of LRP prevents an immediate answer to a question such as "What are the chances that the LRP associated with decision D will exceed X dollars?" In a situation such as this, the first thought is to use Monte Carlo (i.e., random sampling) in order to provide an approximation to the distribution of LRP. An alternative approach, the use of error propagation formulas based on a Taylor series expansion coupled with a Central Limit Theorem approximation, is discussed.