论文信息 - On distributions whose component ratios are Cauchy

On distributions whose component ratios are Cauchy

Abstract This article considers a class of multivariate (dependent) variables that includes those that are obtained as scale mixtures of elliptically symmetric distributions. We provide a simple, intuitive proof that the ratio of two such variables has a general Cauchy distribution. This result extends the results of DeSilva concerning properties of a certain class of dependent multivariate symmetric stable distributions.

Barry C. Arnold | Patrick L. Brockett

[1] Identifiability for dependent multiple decrement/competing risk models , 1983 .

[2] Ignacy Kotlarski. On Bivariate Random Variables Where The Quotient of Their Coordinates Follows Some Known Distribution , 1964 .

[3] R. G. Laha,et al. ON THE LAWS OF CAUCHY AND GAUSS , 1959 .

[4] P. A. P. Moran,et al. An introduction to probability theory , 1968 .

[5] R G Laha. AN EXAMPLE OF A NONNORMAL DISTRIBUTION WHERE THE QUOTIENT FOLLOWS THE CAUCHY LAW. , 1958, Proceedings of the National Academy of Sciences of the United States of America.

[6] Robert J. Beaver,et al. An Introduction to Probability Theory and Mathematical Statistics , 1977 .

[7] William Feller,et al. An Introduction to Probability Theory and Its Applications , 1951 .

[8] E. J. Williams. Some representations of stable random variables as products , 1977 .

[9] Basil M de Silva,et al. A class of multivariate symmetric stable distributions , 1978 .