Definition:Quantile/Continuous

Definition
Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.

Let $X$ have probability density function $f_X$.

Let $q \in \Z_{\ge 1}$ be a strictly positive integer.

Then for $k \in \Z: 0 < k < q$, $x$ is the $k$th $q$-quantile :

Also see
Some specific examples of quantiles which are often found:


 * Median, where $q = 2$
 * Quartile, where $q = 4$
 * Decile, where $q = 10$
 * Centile, or percentile, where $q = 100$.