Summary
A density function is called isotropic distribution when its density function has spheric simetry. First an isotropic distribution on the two dimensional euclidean space is studied. Lerr be the distance from a point in the plane to the origin of coordinates andx one of its coordinates. Then the density function of the marginal distribution ofr is founded, assuming that the marginal distribution ofx is known. The results are generalized to the n-dimensional euclidean space The case of being the marginal distribution of a variablex i a normal one is studied. Then it is proved that then coordinatesx 1,x 2, ...,x n are normal and independient Some more properties are also proved. Some cases of addition of isotropic vectors are considered.
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Casesnoves, D.M. La adicion de vectores aleatorios isotropos en un espacio deN dimensiones. Trabajos de Estadistica 9, 183–202 (1958). https://doi.org/10.1007/BF03028608
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DOI: https://doi.org/10.1007/BF03028608