A Probabilistic Derivation of Stirling's Formula

Abstract

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. Usually a repetition will occur before we obtain all n distinct alternatives consecutively. We shall show that Stirling's formula can be derived and interpreted as follows: as n--->infinity 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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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1991
Accession Number
ADA241899

Entities

People

  • Hsin-yun Li

Organizations

  • Naval Postgraduate School

Tags

DTIC Thesaurus Topics

  • Applied Mathematics
  • Classification
  • Computing-Related Activities
  • Data Science
  • Department Of Defense
  • Equations
  • Inequalities
  • Information Science
  • Interdisciplinary Science
  • Mathematical Analysis
  • Mathematics
  • Notation
  • Probability
  • Random Variables
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Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Regression Analysis.