A general treatment of alternative expectation formulae
Accepted version
Peer-reviewed
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Abstract
The moment of a positive random variable can be obtained by using the survival function. In this paper, we extend existing studies by giving formulae of the expectation of a more general function with respect to a random variable by using either cumulative distribution function or survival function. Both univariate and multivariate examples are given. These formulae can evaluate the expectation when obtaining the probability density/mass function is difficult.
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Keywords
Expectation, Singular distribution, Cumulative distribution function, Survival function, Monte Carlo simulation
Journal Title
Statistics and Probability Letters
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Journal ISSN
0167-7152
1879-2103
1879-2103
Volume Title
166
Publisher
Elsevier BV