Ellipses in Statistics and Finance
In statistics, a bivariate random vector (X, Y) is jointly elliptically distributed if its iso-density contours — loci of equal values of the density function — are ellipses. The concept extends to an arbitrary number of elements of the random vector, in which case in general the iso-density contours are ellipsoids. A special case is the multivariate normal distribution. The elliptical distributions are important in finance because if rates of return on assets are jointly elliptically distributed then all portfolios can be characterized completely by their mean and variance — that is, any two portfolios with identical mean and variance of portfolio return have identical distributions of portfolio return.
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Famous quotes containing the words ellipses in, statistics and/or finance:
“Making the best of things is ... a damn poor way of dealing with them.... My whole life has been a series of escapes from that quicksand [ellipses in source].”
—Rose Wilder Lane (1886–1968)
“O for a man who is a man, and, as my neighbor says, has a bone in his back which you cannot pass your hand through! Our statistics are at fault: the population has been returned too large. How many men are there to a square thousand miles in this country? Hardly one.”
—Henry David Thoreau (1817–1862)
“There is an enormous chasm between the relatively rich and powerful people who make decisions in government, business, and finance and our poorer neighbors who must depend on these decisions to alleviate the problems caused by their lack of power and influence.”
—Jimmy Carter (James Earl Carter, Jr.)