Quantile function

In probability and statistics, the quantile function, associated with a probability distribution of a random variable, specifies the value of the random variable such that the probability of the variable being less than or equal to that value equals the given probability. It is also called the percent-point function or inverse cumulative distribution function. In probability and statistics, the quantile function, associated with a probability distribution of a random variable, specifies the value of the random variable such that the probability of the variable being less than or equal to that value equals the given probability. It is also called the percent-point function or inverse cumulative distribution function. With reference to a continuous and strictly monotonic distribution function, for example the cumulative distribution function F X : R → [ 0 , 1 ] {displaystyle F_{X}colon R o } of a random variable X, the quantile function Q returns a threshold value x below which random draws from the given c.d.f would fall p percent of the time. In terms of the distribution function F, the quantile function Q returns the value x such that