Skip to main content
SpringerLink
Log in

Single Probability

  • Chapter
  • First Online:
Statistical Models for Proportions and Probabilities

Part of the book series: SpringerBriefs in Statistics ((BRIEFSSTATIST))

  • 2099 Accesses

Abstract

The Binomial distribution and its properties are discussed in detail including maximum likelihood estimation of the probability \(p\). Exact and approximate hypothesis tests and confidence intervals are provided for \(p\). Inverse sampling and the Negative Binomial Distribution are also considered.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 29.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    See, for example, http://www.ppsw.rug.nl/~boomsma/confbin.pdf.

  2. 2.

    See also Fay (2010).

References

  • Agresti, A. (2007). An introduction to categorical data analysis. Hoboken, NJ: Wiley Interscience.

    Book  MATH  Google Scholar 

  • Agresti, A., & Caffo, B. (2000). Simple and effective confidence intervals for proportions and differences of proportions result from adding two successes and two failures. The American Statistician, 54(4), 280–288.

    MathSciNet  MATH  Google Scholar 

  • Agresti, A., & Coull, B. A. (1998). Approximate is better than ‘exact’ for interval estimation of binomial proportions. The American Statistician, 52(2), 119–126.

    MathSciNet  Google Scholar 

  • Berry, G., & Armitage, P. (1995). Mid-P confidence intervals: A brief review. The Statistician, 44(4), 417–423.

    Article  Google Scholar 

  • Brown, L. D., Cai, T. T., & DasGupta, A. (2001). Interval estimation of a binomial proportion. Statistical Science 16(2), 101–133.

    Google Scholar 

  • Brown, L. D., Cai, T. T., & DasGupta, A. (2002). Confidence intervals for a binomial proportion and asymptotic expansions. The Annals of Statistics, 30(1), 160–210.

    Article  MathSciNet  MATH  Google Scholar 

  • Clopper, C., & Pearson, E. S. (1934). Ordered and unordered estimators in sampling without replacement. Sankhyā, 18, 379–390.

    Google Scholar 

  • Fay, M. P. (2010). Two-sided exact tests and matching confidence intervals for discrete data. The R Journal 2, 53–58. (See also http://journal.rproject.org/archive/2010-1/RJournal_2010-1_Fay.pdf)

  • Hirji, K. F. (2006). Exact analysis of discrete data. Boca Raton, FL: Taylor and Francis.

    MATH  Google Scholar 

  • Hwang, J. T. G., & Yang, M.-C. (2001). An optimality theory for mid \(p\)-values in \(2 \times 2\) contingency tables. Statistica Sinica, 11, 807–826.

    MathSciNet  MATH  Google Scholar 

  • Johnson, N. L., Kemp, A. W., & Kotz, S. (2005). Univariate discrete distributions (3rd ed.). New York: Wiley.

    Book  MATH  Google Scholar 

  • Jowett, D. H. (1963). The relationship between the binomial and F distributions. The Statistician, 3(1), 55–57.

    Article  Google Scholar 

  • Murthy, M. N. (1957). Ordered and unordered estimators in sampling without replacement. Sankhyā, 18, 379–390.

    MathSciNet  MATH  Google Scholar 

  • Newcombe, R. G. (1998). Two-sided confidence intervals for the single proportion: Comparison of seven methods. Statistics in Medicine, 17(8), 857–872.

    Google Scholar 

  • Salehi, M. M., & Seber, G. A. F. (2001). A new proof of Murthy’s estimator which applies to sequential sampling. Australian and New Zealand Journal of Statistics, 43(3), 901–906.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, The University of Auckland, Princes Street 38, Auckland, 1010, New Zealand

    George A. F. Seber

Authors
  1. George A. F. Seber
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to George A. F. Seber .

Rights and permissions

Reprints and permissions

Copyright information

© 2013 The Author(s)

About this chapter

Cite this chapter

Seber, G.A.F. (2013). Single Probability. In: Statistical Models for Proportions and Probabilities. SpringerBriefs in Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39041-8_2

Download citation

Publish with us

Policies and ethics

Search

Navigation