11. Mathematically, the PaR is the quantile of the profit distribution of a portfolio. 12. The differential entropy of a distribution can be defined in terms of its quantile density, specifically: 13. The VaR risk metric summarizes the quantile , a point with a specified probability of greater losses. 14. If the Q Q plot is based on data, there are multiple quantile estimators in use. 15. The quantile function can be expressed in a closed-form expressions using the Lambert W function: 16. Quantile functions may also be characterized as solutions of non-linear ordinary and partial differential equations.17. When is an integer, the-th smallest of the values,, is the quantile estimate. 18. The mathematical forms arising from quantile regression are distinct from those arising in the method of least squares. 19. Expected shortfall is a portfolio value given that a loss is occurring at or below the q-quantile . 20. A normal quantile plot is commonly used to assess the fit of a data set to a normal population.
