Stirling’s Formula for Gamma Functions, Bounds for Ratios of Gamma Functions, Beta Functions and Percentiles of a Studentized Sample Mean: A Synthesis with New Results

Nitis Mukhopadhyay () and Mun S. Son ()
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Nitis Mukhopadhyay: University of Connecticut
Mun S. Son: University of Vermont

Methodology and Computing in Applied Probability, 2016, vol. 18, issue 4, 1117-1127

Abstract: Abstract In the context of Stirling’s formula for gamma functions and bounds for ratios of gamma functions, this work has a threefold purpose: (1) Outline recently published literature; (2) Synthesize techniques and results from Bhattacharjee and Mukhopadhyay (Commun Stat, Theory & Methods 39:1046–1053, 2010) and Mukhopadhyay (Commun Stat, Theory & Methods 40:1283–1297, 2011) which have gone perhaps unnoticed by some recent researchers; and (3) Incorporate new results for beta functions and useful bounds for the percentiles of a Studentized sample mean obtained from a normal distribution. This synthesized review may help in gaining a wider perspective about this area.

Keywords: Beta function; Central limit theorem; Concavity; Convexity; Gamma function; Jensen’s inequality; Primary 33B15; 41A60; Secondary 26D07 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s11009-015-9473-4

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