Other examples of distributions that are not exponential families are the F-distribution, Cauchy distribution, hypergeometric distribution and logistic distribution.
32.
Other examples of unimodal distributions include Cauchy distribution, Student's t-distribution, chi-squared distribution and exponential distribution.
33.
Some authors define \ mu and \ sigma as the location and scale parameters, respectively, of the log-Cauchy distribution.
34.
It has the standard resonance form of the Lorentz, or Cauchy distribution, but involves relativistic variables = ? here = 2.
35.
This is the characteristic function of the standard Cauchy distribution : thus, the sample mean has the same distribution as the population itself.
36.
For \ mu = 0 and \ sigma = 1, corresponding to a standard Cauchy distribution, the probability density function reduces to:
37.
Generally, a "'Cauchy distribution "'is any probability distribution belonging to the same location-scale family as this one.
38.
If a continuous distribution does not have an expected value, as is the case for the Cauchy distribution, it does not have a variance either.
39.
Like all stable distributions, the location-scale family to which the Cauchy distribution belongs is closed under linear transformations with linear fractional transformations with real coefficients.
40.
However, because of the fat tails of the Cauchy distribution, the efficiency of the estimator decreases if more than 24 % of the sample is used.
