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Activity Number:
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66
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Type:
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Contributed
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Date/Time:
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Sunday, August 2, 2009 : 4:00 PM to 5:50 PM
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Sponsor:
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IMS
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| Abstract - #303283 |
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Title:
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Stirling's Formula and Its Extensions: Heuristic Approaches
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Author(s):
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Debanjan Bhattacharjee*+
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Companies:
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University of Connecticut
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Address:
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Department of Statistics, Storrs, CT, 06269,
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Keywords:
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Binomial coefficient ; Gamma function ; Multinomial coefficient ; Negative binomial coefficient ; Normal approximation ; Stirling's approximation
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Abstract:
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Walsh (1995) introduced a heuristic approach to motivate Stirling's formula by manipulating Poisson probability. We explore similar heuristics in other problems involving approximations for interesting binomial and negative binomial coefficients. The scope of this approach is then broadened to approximate interesting multinomial coefficients. Also included is an approximation for $(nk)!$ where $n$ (large) and $k$ are positive integers using heuristics that are markedly different from Walsh's. We demonstrate how such heuristics can validate Stirling's formula for $\Gamma(n\alpha)$ where $n$ is a large positive integer but $\alpha (>0) is arbitrary. Throughout this investigation, we have emphasized a direct approach.
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