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Fractiles of Random Variables

In: Introduction to Probability and Statistics for Engineers

Author

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  • Milan Holický

    (Czech Technical University in Prague, Klokner Institute, Department of Structural Reliability)

Abstract

A fractile is the value of a random variable corresponding to a given probability of occurrence of values smaller than the fractile. It is an important concept used in many engineering and scientific applications. If a random variable is defined by a known theoretical model then the fractile is simply the point at which the distribution function attains the specified probability. However, estimation of fractiles from limited sample data without having a theoretical model of the random variable is a more complicated task. Two different methods are commonly used: the classical coverage method and the prediction method. Operational techniques are provided for both methods and their comparison, taking into account the confidence level of the coverage method offered. In addition, the Bayessian approach to fractile estimation is explained, by way of updating prior data with newly obtained information. A review of fundamental procedures provides Annex 5.

Suggested Citation

  • Milan Holický, 2013. "Fractiles of Random Variables," Springer Books, in: Introduction to Probability and Statistics for Engineers, edition 127, chapter 0, pages 109-123, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-38300-7_9
    DOI: 10.1007/978-3-642-38300-7_9
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