Quantile

In Statistics, a Quantile is a statistical value that divides a Probability Distribution into equally weighted continuous intervals.

• Percentile, divide into 100 equal parts
• Quartile, divide in 4 equal parts
• $1-\alpha$ Quantile
  • $T_{1-\alpha }:X\in \text{RV}\to x_{\alpha }\text{s.t.}P(X>x_{\alpha })=1-F(x_{\alpha })=\alpha$
  • where $F$ is the CDF