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A unified method for constructing expectation tolerance intervals

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  • Christopher Withers
  • Saralees Nadarajah

Abstract

Given a random sample of size $$n$$ n with mean $$\overline{X} $$ X ¯ and standard deviation $$s$$ s from a symmetric distribution $$F(x; \mu , \sigma )=F_{0} (( x- \mu ) / \sigma ) $$ F ( x ; μ , σ ) = F 0 ( ( x - μ ) / σ ) with $$F_0$$ F 0 known, and $$X \sim F(x;\; \mu , \sigma )$$ X ∼ F ( x ; μ , σ ) independent of the sample, we show how to construct an expansion $$ a_n^{\prime }=\sum _{i=0}^\infty \ c_i \ n^{-i} $$ a n ′ = ∑ i = 0 ∞ c i n - i such that $$\overline{X} - s a_n^{\prime } > X > \overline{X} + s a_n^{\prime } $$ X ¯ - s a n ′ > X > X ¯ + s a n ′ with a given probability $$\beta $$ β . The practical value of this result is illustrated by simulation and using a real data set. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Christopher Withers & Saralees Nadarajah, 2014. "A unified method for constructing expectation tolerance intervals," Statistical Papers, Springer, vol. 55(4), pages 951-965, November.
    • Handle: RePEc:spr:stpapr:v:55:y:2014:i:4:p:951-965
    DOI: 10.1007/s00362-013-0543-9
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    References listed on IDEAS

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    1. Lin, Tsai-Yu & Liao, Chen-Tuo, 2006. "A [beta]-expectation tolerance interval for general balanced mixed linear models," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 911-925, February.
    2. Haq, M. Safiul & Rinco, Stefan, 1976. "[beta]-Expectation tolerance regions for a generalized multivariate model with normal error variables," Journal of Multivariate Analysis, Elsevier, vol. 6(3), pages 414-421, September.
    3. D. T. Shirke & R. R. Kumbhar & D. Kundu, 2005. "Tolerance intervals for exponentiated scale family of distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(10), pages 1067-1074.
    4. Shahjahan Khan, 2009. "Optimal tolerance regions for future regression vector and residual sum of squares of multiple regression model with multivariate spherically contoured errors," Statistical Papers, Springer, vol. 50(3), pages 511-525, June.
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