| Author/Editor | Cedilnik, Anton; Košmelj, Katarina; Blejec, Andrej | |
| Title | The distribution of the ration of jointly normal variables | |
| Type | članek | |
| Source | Metodol Zv Ljubl | |
| Vol. and No. | Letnik 1, št. 1 | |
| Publication year | 2004 | |
| Volume | str. 99-108 | |
| Language | eng | |
| Abstract | We derive the probability density of the ratio of components of the bivariate normal distribution with arbitrary parameters. The density is a product of two factors, the first is a Cauchy density, the second a very complicated function. We show that the distribution under study does not possess an expected value or other moments of higher order. Our particular interest is focused on Ihe shape of the density. We introducc a shape parameter and show that according to its sign the densities are classified into three main groups. As an example, we derive the distribution of the ratio Z =-Bm-1/(mBm) for a polynomial regression of order m. For m=1, Z is the estimator for the zero of a linear regression, for m=2, an estimator for the abscissa of the extreme of a quadratic regression, and for m=3, an estimator for the abscissa of the inf7ection point of a cubic regression. | |
| Descriptors | NORMAL DISTRIBUTION PROBABILITY |