Stirling’s Approximation for Factorials — Proof and Applications
<p>Factorial is one of the ubiquitous concepts in mathematics. It is also an important mathematical concept used in data science. For modeling probability distributions in the Poisson process, factorial is used. The probability mass function of the Poisson distribution has factorial expression in the denominator. We would not be able to find the probability of some Poisson random variable without having a way to compute factorial.</p>
<p>Factorial has a relationship with combinatorics too. For example, <em>n!</em> is the number of permutations of <em>n</em> unique objects. Entropy is defined as a combinatorial problem from the view of statistical mechanics. Entropy also has a separate definition in information theory. When two alternative definitions are compared, they are identical.</p>
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