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Fuzzy Statistics

  • Book
  • © 2004

Overview

Authors:
  1. James J. Buckley

    1. Mathematics Department, University of Alabama at Birmingham, Birmingham, USA

    View author publications

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  • Starting from basic statistics leading to fuzzy statistics,
  • appealing to statisticians as well as researchers in fuzziness
  • Includes supplementary material: sn.pub/extras

Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 149)

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Table of contents (29 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Introduction

    • James J. Buckley
    Pages 1-4

  3. Fuzzy Sets

    • James J. Buckley
    Pages 5-16

  4. Estimate μ, Variance Known

    • James J. Buckley
    Pages 17-22

  5. Estimate μ, Variance Unknown

    • James J. Buckley
    Pages 23-26

  6. Estimate p, Binomial Population

    • James J. Buckley
    Pages 27-30

  7. Estimate σ2 from a Normal Population

    • James J. Buckley
    Pages 31-36

  8. Estimate µ 1 — µ 2, Variances Known

    • James J. Buckley
    Pages 37-38

  9. Estimate μ 1 — μ 2, Variances Unknown

    • James J. Buckley
    Pages 39-42

  10. Estimate d =μ 1 — μ 2, Matched Pairs

    • James J. Buckley
    Pages 43-45

  11. Estimate p 1 — p 2, Binomial Populations

    • James J. Buckley
    Pages 47-48

  12. Estimate σ 1 2 /σ 2 2 , Normal Populations

    • James J. Buckley
    Pages 49-52

  13. Tests on µ, Variance Known

    • James J. Buckley
    Pages 53-59

  14. Tests on µ, Variance Unknown

    • James J. Buckley
    Pages 61-67

  15. Tests on p for a Binomial Population

    • James J. Buckley
    Pages 69-72

  16. Tests on σ 2, Normal Population

    • James J. Buckley
    Pages 73-76

  17. Tests μ 1 verses μ 2, Variances Known

    • James J. Buckley
    Pages 77-79

  18. Test μ 1 verses μ 2, Variances Unknown

    • James J. Buckley
    Pages 81-90

  19. Test p 1 = p 2, Binomial Populations

    • James J. Buckley
    Pages 91-93

  20. Test d = µ 1 — µ 2 , Matched Pairs

    • James J. Buckley
    Pages 95-98
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Keywords

About this book

1. 1 Introduction This book is written in four major divisions. The first part is the introductory chapters consisting of Chapters 1 and 2. In part two, Chapters 3-11, we develop fuzzy estimation. For example, in Chapter 3 we construct a fuzzy estimator for the mean of a normal distribution assuming the variance is known. More details on fuzzy estimation are in Chapter 3 and then after Chapter 3, Chapters 4-11 can be read independently. Part three, Chapters 12- 20, are on fuzzy hypothesis testing. For example, in Chapter 12 we consider the test Ho : /1 = /10 verses HI : /1 f=- /10 where /1 is the mean of a normal distribution with known variance, but we use a fuzzy number (from Chapter 3) estimator of /1 in the test statistic. More details on fuzzy hypothesis testing are in Chapter 12 and then after Chapter 12 Chapters 13-20 may be read independently. Part four, Chapters 21-27, are on fuzzy regression and fuzzy prediction. We start with fuzzy correlation in Chapter 21. Simple linear regression is the topic in Chapters 22-24 and Chapters 25-27 concentrate on multiple linear regression. Part two (fuzzy estimation) is used in Chapters 22 and 25; and part 3 (fuzzy hypothesis testing) is employed in Chapters 24 and 27. Fuzzy prediction is contained in Chapters 23 and 26. A most important part of our models in fuzzy statistics is that we always start with a random sample producing crisp (non-fuzzy) data.

Authors and Affiliations

  • Mathematics Department, University of Alabama at Birmingham, Birmingham, USA

    James J. Buckley

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