The Normal Distribution
The normal distribution is perhaps the most important case. Because the normal distribution is a location-scale family, its quantile function for arbitrary parameters can be derived from a simple transformation of the quantile function of the standard normal distribution, known as the probit function. Unfortunately, this function has no closed-form representation using basic algebraic functions; as a result, approximate representations are usually used. Thorough composite rational and polynomial approximations have been given by Wichura and Acklam (see his web site in External Links). Non-composite rational approximations have been developed by Shaw (see Monte Carlo recycling in External Links).
Read more about this topic: Quantile Function
Famous quotes containing the words normal and/or distribution:
“What strikes many twin researchers now is not how much identical twins are alike, but rather how different they are, given the same genetic makeup....Multiples don’t walk around in lockstep, talking in unison, thinking identical thoughts. The bond for normal twins, whether they are identical or fraternal, is based on how they, as individuals who are keenly aware of the differences between them, learn to relate to one another.”
—Pamela Patrick Novotny (20th century)
“Classical and romantic: private language of a family quarrel, a dead dispute over the distribution of emphasis between man and nature.”
—Cyril Connolly (1903–1974)