Equating Poisson and Normal Probability Functions to Derive Stirling's Formula |
| |
Authors: | Dennis P. Walsh |
| |
Affiliation: | Department of Mathematics and Statistics , Middle Tennessee State University , Murfreesboro , TN , 37132 , USA |
| |
Abstract: | Often texts for introductory courses in probability or mathematical statistics make reference to Stirling's asymptotic formula (for a factorial) without presenting any proof or justification for the formula. A notable exception is Feller. In this article, we present a derivation of Stirling's formula based on the normal approximation of a Poisson probability that is considerably more accessible to the average student than Feller's approach. Besides illustrating a usage of the central limit theorem in conjunction with a continuity correction, the derivation lends itself to a mnemonic device for quickly obtaining Stirling's formula. |
| |
Keywords: | Central limit theorem Continuity correction |
|
|