An unusual application of Cramér-Rao inequality to prove the attainable lower bound for a ratio of complicated gamma functions

DOI10.1007/s11009-020-09822-wzbMath1498.60079OpenAlexW3091064959MaRDI QIDQ2065485

Nitis Mukhopadhyay, Srawan Kumar Bishnoi

Publication date: 7 January 2022

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

Full work available at URL: https://doi.org/10.1007/s11009-020-09822-w

zbMATH Keywords

asymptotic distributionstopping timeCramér-Rao inequalityconfidence intervalpoint estimationCLTgamma functionsrandom CLT

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Central limit and other weak theorems (60F05) Gamma, beta and polygamma functions (33B15) Stopping times; optimal stopping problems; gambling theory (60G40)

Related Items

An optimal purely sequential strategy with asymptotic second-order properties: Applications from statistical inference and data analysis

Cites Work

• On a sharper lower bound for a percentile of a Student's \(t\) distribution with an application
• On asymptotic and strict monotonicity of a sharper lower bound for Student's \(t\) percentiles
• Second order approximations for sequential point and interval estimation
• A nonlinear renewal theory with applications to sequential analysis. I
• A nonlinear renewal theory with applications to sequential analysis II
• Some recent results on the distributions of stopping times of compound Poisson processes with linear boundaries
• Modified Linex two-stage and purely sequential estimation of the variance in a normal distribution with illustrations using horticultural data
• 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
• Sample path analysis and distributions of boundary crossing times
• On Sharp Jensen's Inequality and Some Unusual Applications
• Stage‐Wise Adaptive Designs
• Sequential estimation problems for negative exponential populations
• Sequential Methods and Their Applications
• A Note on Minimum Variance Unbiased Estimation
• On Exact and Asymptotic Properties of Two-Stage and Sequential Estimation of the Normal Mean Under LINEX Loss
• Computation of the Gamma, Digamma, and Trigamma Functions
• EDA on the asymptotic normality of the standardized sequential stopping times, Part-I: Parametric models
• A Precision Approximation of the Gamma Function
• On the Asymptotic Theory of Fixed-Width Sequential Confidence Intervals for the Mean
• On the Asymptotic Efficiency of a Sequential Procedure for Estimating the Mean
• Linear Statistical Inference and its Applications
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item