Tomasz Rychlik

Projecting Statistical Functionals (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book presents a method of establishing explicit solutions to classical problems of calculating the best lower and upper mean-variance bounds. The following families of distributions are taken into account: arbitrary, symmetric, symmetric unimodal, and U-shaped. The book is addressed to students, researchers, and practitioners in statistics and applied probability. Most of the results are recent, and a significant part of them has not been published yet. Numerous open problems are stated in the text.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 175
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461220947
• Artikelnr.: 43987234

Inhaltsangabe

1 Introduction and Notation.- 1.1 Introduction.- 1.2 Notation.- 2 Basic Notions.- 2.1 Elements of Hilbert Space Theory.- 2.2 Statistical Linear Functionals.- 2.3 Restricted Families of Distributions.- 3 Quantiles.- 3.1 General and Symmetric Distributions.- 3.2 Distributions with Monotone Density and Failure Rate.- 3.3 Distributions with Monotone Density and Failure Rate on the Average.- 3.4 Symmetric Unimodal Distributions.- 3.5 Open Problems.- 4 Order Statistics of Independent Samples.- 4.1 General and Symmetric Distributions.- 4.2 Life Distributions with Decreasing Density and Failure Rate.- 4.3 Distributions with Monotone Density and Failure Rate on the Average.- 4.4 Symmetric Unimodal Distributions.- 4.5 Bias of Quantile Estimates.- 4.6 Open Problems.- 5 Order Statistics of Dependent Observations.- 5.1 Dependent Observations with Given Marginal Distribution.- 5.2 General and Symmetric Distributions.- 5.3 Distributions with Monotone Density and Failure Rate.- 5.4 Distributions with Monotone Density and Failure Rate on the Average.- 5.5 Symmetric Unimodal and U-Shaped Distributions.- 5.6 Bias of Quantile Estimates.- 5.7 Extreme Effect of Dependence.- 5.8 Open Problems.- 6 Records and kth Records.- 6.1 Dependent Identically Distributed Observations.- 6.2 General and Symmetric Distributions.- 6.3 Life Distributions with Decreasing Density and Failure Rate.- 6.4 Increments of Records.- 6.5 Open Problems.- 7 Predictions of Order and Record Statistics.- 7.1 General Distributions.- 7.2 Distributions with Decreasing Density and Failure Rate.- 7.3 Open Problems.- 8 Further Research Directions.- References.- Author Index.