Bounding the Results of Arithmetic Operations on Random Variables of Unknown Dependency Using Intervals
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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.
KeywordsMathematical Modeling Distribution Function Cancer Risk Computational Mathematic Additional Data
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