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Confidence intervals for the ratio of two means using the distribution of the quotient of two normals

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  • Carlotta Galeone
  • Angiola Pollastri

Abstract

In various scientific fields such as medicine, biology and bioassay, several ratio quantities assumed to be Normal, are of potential interest. The estimator of the ratio of two means is a ratio of two random variables normally or asymptotically normally distributed. The present paper shows the importance of considering the real distribution of the estimator of the ratio of two means, because generally the approximation to Normal is not satisfied. The estimated asymptotic cumulative and density function of the estimator of the ratio is presented, with several considerations on the skewness. Finally, a new method for building confidence intervals for the ratio of two means was proposed. In contrast to other parametric methods, this new method is worthy to be preferred because it considers the skewness in the distribution of the ratio estimator, and the confidence intervals are always bounded.

Suggested Citation

  • Carlotta Galeone & Angiola Pollastri, 2012. "Confidence intervals for the ratio of two means using the distribution of the quotient of two normals," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 13(3), pages 451-472, December.
    • Handle: RePEc:csb:stintr:v:13:y:2012:i:3:p:451-472
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    References listed on IDEAS

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    1. Marsaglia, George, 2006. "Ratios of Normal Variables," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 16(i04).
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    Cited by:

    1. Angiola Pollastri & Walter Maffenini, 2018. "Estimation of the Percentage of Aid Received from the Food Bank Using a Stratified Sampling," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 136(1), pages 41-49, February.

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