On a sharper lower bound for a percentile of a Student's \(t\) distribution with an application

DOI10.1007/s11009-009-9127-5zbMath1204.60021OpenAlexW2043646024MaRDI QIDQ607606

Nitis Mukhopadhyay

Publication date: 22 November 2010

Published in: Methodology and Computing in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11009-009-9127-5

zbMATH Keywords

confidence intervalsJensen's inequalitysimulationsdiagnosticsfixed-width confidence intervalsaverage sample sizenon-central \(t\)-distributionStudent's \(t\)-distributioncentral \(t\)-distributioncompare percentilesoversampling percentagepilot sample sizestandard normaltwo-stage sampling

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Exact distribution theory in statistics (62E15) Probability distributions: general theory (60E05)

Related Items

Lower Bounds for Percentiles of Pivots from a Sample Mean Standardized by S, the GMD, the MAD, or the Range in a Normal Distribution and Miscellany with Data Analysis, 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, On asymptotic and strict monotonicity of a sharper lower bound for Student's \(t\) percentiles, An unusual application of Cramér-Rao inequality to prove the attainable lower bound for a ratio of complicated gamma functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Errors in Normal Approximations to the $t,\tau,$ and Similar Types of Distribution
• The Percentile Points of Distributions Having Known Cumulants
• Bounds on Normal Approximations to Student's and the Chi-Square Distributions
• A modification of the Fisher-Cornish approximation for the student t percentiles
• Sequential Methods and Their Applications
• A Study of the Accuracy of Some Approximations for t, χ 2 , and F Tail Probabilities
• Power of the Noncentral F-Test: Effect of Additional Variates on Hotelling's T 2 -Test
• On the Non-Existence of Tests of "Student's" Hypothesis Having Power Functions Independent of $\sigma$
• A Two-Sample Test for a Linear Hypothesis Whose Power is Independent of the Variance