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

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

Philipp Wacker (Contact Author)

University of Canterbury ( email )

Ilam Road
Christchurch 8140
New Zealand

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