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Bounding the Results of Arithmetic Operations on Random Variables of Unknown Dependency Using Intervals

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Reliable Computing

Abstract

Many real problems involve calculations on random variables, yet precise details about the correlations or other dependency relationships among those variables are often unknown.

For example consider analyzing the cancer risk associated with an environmental contaminant. The dependency of an individual's cumulative exposure on the less useful (but more obtainable) current exposure level will be uncertain. In this and many other cases, data points from which to derive such dependencies are sparse, and obtaining additional data is prohibitively expensive or difficult. Thus manipulating variables whose dependencies are unspecified is a problem of significance.

This paper describes a new approach to bounding the results of arithmetic operations on random variables when the dependency relationship between the variables is unspecified. The bounds enclose the space in which the result's distribution function can be.

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Authors and Affiliations

  1. University of Arkansas, 313 Engineering Hall, Fayetteville, AR, 72701, USA, e-mail

    Daniel Berleant & Chaim Goodman-Strauss

Authors
  1. Daniel Berleant
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  2. Chaim Goodman-Strauss
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Berleant, D., Goodman-Strauss, C. Bounding the Results of Arithmetic Operations on Random Variables of Unknown Dependency Using Intervals. Reliable Computing 4, 147–165 (1998). https://doi.org/10.1023/A:1009933109326

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