McCullagh's Parametrization of the Cauchy Distributions | Probability theory, Cauchy distribution, Probability distribution, Probability density function, Real number, Median, Location- scale family. Este artículo no está disponible.McCullagh's Parametrization of the Cauchy Distributions | Probability theory, Cauchy distribution, Probability distribution, Probability density function, Real number, Median, Location- scale family

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In probability theory, the standard" Cauchy distribution is the probability distribution whose probability density function is f(x) = {1 over pi (1 + x^2)} for x real. This has median 0, and first and third quartiles respectively -1 and +1. Generally, a Cauchy distribution is any probability distribution belonging to the same location-scale family as this one. Thus, if X has a standard Cauchy distribution and u is any real number and o > 0, then Y = u + oX has a Cauchy distribution whose median is u and whose first and third quartiles are respectively u – o and u + o. McCullagh''s parametrization, introduced by Peter McCullagh, professor of statistics at the University of Chicago uses the two parameters of the non-standardised distribution to form a single complex-valued parameter, specifically, the complex number 0 = u + io, where i is the imaginary unit. It also extends the usual range of scale parameter to include 0 < 0. "

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In probability theory, the standard" Cauchy distribution is the probability distribution whose probability density function is f(x) = {1 over pi (1 + x^2)} for x real. This has median 0, and first and third quartiles respectively -1 and +1. Generally, a Cauchy distribution is any probability distribution belonging to the same location-scale family as this one. Thus, if X has a standard Cauchy distribution and u is any real number and o > 0, then Y = u + oX has a Cauchy distribution whose median is u and whose first and third quartiles are respectively u – o and u + o. McCullagh''s parametrization, introduced by Peter McCullagh, professor of statistics at the University of Chicago uses the two parameters of the non-standardised distribution to form a single complex-valued parameter, specifically, the complex number 0 = u + io, where i is the imaginary unit. It also extends the usual range of scale parameter to include 0 < 0. "