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Boundary Conditions for Ratios with Positively Distributed Components
Authors:Stuart McLeay
Institution:University of Wales, Bangor
Abstract:This paper describes the statistical properties of the ratio of two positively distributed variables where the numerator is a component of the denominator and where, therefore, the ratio has implicit boundaries of 0 and 1. Johnson's bounded distribution (the SB) is suggested as a model for ratios of this type, and is derived in this paper as a ratio of lognormal variates. An empirical analysis of bounded financial ratios of UK companies confirms the goodness of fit.
Keywords:financial ratios  statistical distributions  Johnson system  boundary conditions  maximum likelihood
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