abstract: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 function (pdf) or probability mass function, the cumulative distribution function (cdf) and the characteristic function.