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Simple Statistical Derivations of the Stirling’s Formula Using Normal Approximations and Laplace’s Method |
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PP: 27-31 |
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doi:10.18576/jsapl/040104
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Author(s) |
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Jose Guardiola,
Hassan Elsalloukh,
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Abstract |
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| In this article we show several methods that are useful to introduce students to the derivation of Stirling’s formula. The methods shown here use the normal density as the limiting distribution to other distributions. The last procedure uses Laplace’s method by completing a definite integral to the kernel of a normal distribution in order to solve it. The advantages of these procedures over many others found in the literature are their simplicity and their relationship with a normal limiting distribution. Under this approach, Laplace’s method can also be considered as an approximation to a normal distribution to obtain the derivation of Stirling’s formula. The derivations shown here are simple enough and sufficiently short such that they can be used for educational purposes on some undergraduate courses in statistics. |
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