Please, Not Another Note About Generalized Inverses
11 Pages Posted: 23 Aug 2023
Abstract
We prove some statements of left- and right-continuous variants of generalized inverses of non-decreasing real functions. This allows us to derive a general formula for the distribution of F◦X, where X is a random variable and F is its probability distribution function. This was previously known only for the case where F is continuous.
Keywords: generalized inverse, distribution function, quantile function, survival function, inverse transform sampling
Suggested Citation: Suggested Citation
Wacker, Philipp, Please, Not Another Note About Generalized Inverses. Available at SSRN: https://ssrn.com/abstract=4549719 or http://dx.doi.org/10.2139/ssrn.4549719
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