Some bounds on the distribution functions of linear combinations and applications

DOI10.1007/BF02532777zbMath0429.62014OpenAlexW1999069233MaRDI QIDQ1137831

Siddhartha R. Dalal, Govind S. Mudholkar

Publication date: 1977

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02532777

zbMATH Keywords

boundsBehrens Fisher problemdistribution of linear combinations

Mathematics Subject Classification ID

Parametric hypothesis testing (62F03) Exact distribution theory in statistics (62E15)

Cites Work

• A generalized monotone character of d.f.'s and moments of statistics from some well-known populations
• The Integral of a Symmetric Unimodal Function over a Symmetric Convex Set and Some Probability Inequalities
• On Linear Combinations of Several Variances
• Some Concepts of Dependence
• Bounds on the Distribution Functions of the Behrens-Fisher Statistic
• Some Inequalities for Central and Non-Central Distributions
• The integral of an invariant unimodal function over an invariant convex set—an inequality and applications
• On the Distribution of a Linear Combination of Independent Chi Squares
• On a New Class of Bounds for the Distribution of Quadratic Forms in Normal Variates
• Application of the Method of Mixtures to Quadratic Forms in Normal Variates
• A Note on the Convolution of Uniform Distributions
• Some Theorems on Quadratic Forms Applied in the Study of Analysis of Variance Problems, I. Effect of Inequality of Variance in the One-Way Classification

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