Calculation
The evaluation of quantile functions often involves numerical methods, as the example of the exponential distribution above is one of the few distributions where a closed-form expression can be found (others include the uniform, the Weibull, the Tukey lambda (which includes the logistic) and the log-logistic). When the cdf itself has a closed-form expression, one can always use a numerical root-finding algorithm such as the bisection method to invert the cdf. Other algorithms to evaluate quantile functions are given in the Numerical Recipes series of books. Algorithms for common distributions are built in to many statistical software packages.
Quantile functions may also be characterized as solutions of non-linear ordinary and partial differential equations. The ordinary differential equations for the cases of the normal, Student, beta and gamma distributions have been given and solved.
Read more about this topic: Quantile Function
Famous quotes containing the word calculation:
“Common sense is the measure of the possible; it is composed of experience and prevision; it is calculation appled to life.”
—Henri-Frédéric Amiel (1821–1881)
““To my thinking” boomed the Professor, begging the question as usual, “the greatest triumph of the human mind was the calculation of Neptune from the observed vagaries of the orbit of Uranus.”
“And yours,” said the P.B.”
—Samuel Beckett (1906–1989)