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A Survey of Estimating Distributional Parameters and Sample Sizes from Truncated Samples

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Statistical Distributions in Scientific Work

Part of the book series: NATO Advanced study Institutes Series ((ASIC,volume 79))

Summary

Suppose X1,…, XN are independent random variables with common distribution F(x;θ). We observe Xi only if it lies outside a given region R. Thus the number n of observed X’s is a binomial (N,P) variate, where P = 1 — P(X in R). Based on n and the values of the observed X’s, we want to estimate N and θ. Conditional and unconditional maximum likelihood estimators and modifications of these will be discussed. Asymptotic results of both first and second order will be considered, and small sample results also mentioned. Sequential and two stage results will receive brief coverage. A variety of applications will be given.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois, 61801, USA

    Saul Blumenthal

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  1. Saul Blumenthal
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Editor information

Editors and Affiliations

  1. Department of Statistics, The pennsylvania State University, University Park, Pennsylvania, USA

    Charles Taillie  & Ganapati P. Patil  & 

  2. Instituto di Calcolo delle Probabilità, Facoltà di Scienze Statistische Demografiche e Attuariali, Università degli Studi di Roma, Italy

    Bruno A. Baldessari

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© 1981 D. Reidel Publishing Company

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Blumenthal, S. (1981). A Survey of Estimating Distributional Parameters and Sample Sizes from Truncated Samples. In: Taillie, C., Patil, G.P., Baldessari, B.A. (eds) Statistical Distributions in Scientific Work. NATO Advanced study Institutes Series, vol 79. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8552-0_6

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  • DOI: https://doi.org/10.1007/978-94-009-8552-0_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-8554-4

  • Online ISBN: 978-94-009-8552-0

  • eBook Packages: Springer Book Archive

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