A probabilistic derivation of Stirling's formula.

62 Pages·0.44 MB·en_US

by  Li, Hsin-Yun.;Frenzen, Christopher L.

NAVAL POSTGRADUATE SCHOOL
Monterey
California
,
THESIS
A PROBABILISTIC DERIVATION
OF
STIRLING'S FORMULA
by
Li, Hsin-Yun
March 1991
Thesis Advisor: C. L. Frenzen
Approved for public release; distribution is unlimited.
T2 53644

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11 TITLE (Include Security Classification)
A PROBABILISTIC DERIVATION OF STIRLING'S FORMULA
12 PERSONAL AUTHOR(S)
Li, Hsin-Yun
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Master's Thesis FROM TO March 1991 48
16 supplementary notation The views expressed in this thesis are those of the author and do
not reflect the official policy or position of the Department of Defense or the U.S. Gov,
17 COSATI CODES 18 SUBJECT TERMS (Continue on reverse if necessary and identify by block number)
FIELD GROUP SUB-GROUP Asymptotic analysis, Probability, Combinatorial, and
Calculus
19 ABSTRACT (Continue on reverse if necessary and identify by block number)
Stirling's formula- is one of the most frequently used results from asymptotics. It is
used in probability and statistics, algorithm analysis and physics. In this thesis we
shall give a new probabilistic derivation of Stirling's formula. Our motivation comes
from sampling randomly with replacement from a group of n distinct alternatives.
U. ually a repetition will occur before we obtain all n distinct alternatives consec-
ui Lvely. We shall show that Stirling's formula can be derived and interpreted as
follows: as n >°° the expected total number of distinct alternatives we must sample
before all n are obtained consecutively is asymptotically equal to the expected number
of attempts we make to obtain all n distinct alternatives consecutively times the
expected number of distinct alternatives obtained per attempt.
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Approved for public release; distribution is unlimited.
A Probabilistic Derivation of Stirling's Formula
by
Li, Hsin-Yun
LCDR, Republic of China Navy
B.S., Chinese Naval Academy, 1980
Submitted in partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE IN APPLIED MATHEMATICS
from the
NAVAL POSTGRADUATE SCHOOL
March 1991
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