Ratios of Normal Variables
By George Marsaglia. 2006
212 citations recorded by the source corpus.
This article extends and amplifies on results from a paper of over forty years ago. It provides software for evaluating the density and distribution functions of the ratio z/w for any two jointly normal variates z,w, and provides details on methods for transforming a general ratio z/w into a standard form, (a+x)/(b+y) , with x and y independent standard normal and a, b non-negative constants. It discusses handling general ratios when, in theory, none of the moments exist yet practical considerations suggest there should be approximations whose adequacy can be verified by means of the included software. These approximations show that many of the ratios of normal variates encountered in practice can themselves be taken as normally distributed. A practical rule is developed: If a
Subfields: Computational Mechanics, Statistical and Nonlinear Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/041e3e70f41511647502141e6c9a457436f2d13b
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In Computational Mechanics
In Statistical and Nonlinear Physics
In Statistics and Probability
Citations in the corpus
- On the existence of a normal approximation to the distribution of the ratio of two independent normal random variables (2013, methodology): “The random variable Z = X/Y has no finite moments and its distribution FZ is heavy tailed (Hinkley, 1969; Marsaglia, 2006).”
- A new baseline model for estimating willingness to pay from discrete choice models (2013, background): “Marsaglia (2006) provides a tighter bound for the ratio variable having an approximate normal distribution that requires the t-statistic on the denominator, C t , be greater than 4 and ( B t”