Representations of characteristic function via survival function and generalized inverse function

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The moment generating function and moments of a real-valued random variable can be expressed in terms of the survival function or inverse survival function. In this article, we give the representation of characteristic function via the generalized inverse survival function or generalized inverse distribution function for arbitrary distributions. We extend existing studies, both univariate and multivariate, by giving formulae of the expectation of a more general function of a random variable. These results have potential applications in a variety of fields. To illustrate their applications, we calculate the characteristic functions of several distributions appear in distortion riskmetrics and weighted entropies.