Quantile Function

In probability and statistics, the quantile function, also called percent point function or inverse cumulative distribution function, of the probability distribution of a random variable specifies, for a given probability, the value which the random variable will be at, or below, with that probability. The quantile function is one way of prescribing a probability distribution, and it is an alternative to the probability density or mass function, the cumulative distribution function and the characteristic function. The quantile function, Q, of a probability distribution is the inverse of its cumulative distribution function (cdf) F. The derivative of the quantile function, namely the quantile density function, is yet another way of prescribing a probability distribution. It is the reciprocal of the pdf composed with the quantile function.