On Asymptotic and Strict Monotonicity of a Sharper Lower Bound for Student’s t Percentiles

Allan Gut () and Nitis Mukhopadhyay ()
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Allan Gut: Uppsala University
Nitis Mukhopadhyay: University of Connecticut

Methodology and Computing in Applied Probability, 2010, vol. 12, issue 4, 647-657

Abstract: Abstract Let z α and t ν,α denote the upper 100α% points of a standard normal and a Student’s t ν distributions respectively. It is well-known that for every fixed $0 z α and that t ν,α monotonically decreases to z α as ν increases. Recently, Mukhopadhyay (Methodol Comput Appl Probab, 2009) found a new and explicit expression b ν ( > 1) such that t ν,α > b ν z α for every fixed $0

Keywords: Asymptotic monotonicity; Gamma function; Percentiles; Standard normal; Strict monotonicity; Student’s t-distribution; Primary 60F15; Secondary 62E15, 62E99 (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11009-009-9128-4

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