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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

Author

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  • Nitis Mukhopadhyay

    (University of Connecticut)

  • Mun S. Son

    (University of Vermont)

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.

Suggested Citation

  • Nitis Mukhopadhyay & Mun S. Son, 2016. "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," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1117-1127, December.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:4:d:10.1007_s11009-015-9473-4
    DOI: 10.1007/s11009-015-9473-4
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    References listed on IDEAS

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    1. Allan Gut & Nitis Mukhopadhyay, 2010. "On Asymptotic and Strict Monotonicity of a Sharper Lower Bound for Student’s t Percentiles," Methodology and Computing in Applied Probability, Springer, vol. 12(4), pages 647-657, December.
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    Cited by:

    1. Giussani, A. & Bonetti, M., 2019. "A note on the length-biased Weibull-Gamma frailty survival model," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 32-36.

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