In probability and statistics, the quantile function outputs the value of a random variable such that its probability is less than or equal to an input probability value. Intuitively, the quantile function associates with a range at and … See more

For example, the cumulative distribution function of Exponential(λ) (i.e. intensity λ and expected value (mean) 1/λ) is
$${\displaystyle F(x;\lambda )={\begin{cases}1-e^{-\lambda x}&x\geq 0,\\0&x<0.\end{cases}}}$$
The quantile … See more

The evaluation of quantile functions often involves numerical methods, such as the exponential distribution above, which is one of the few distributions where a closed-form expression can be found (others include the uniform, the Weibull, the See more

• Inverse transform sampling
• Percentage point
• Probability integral transform
• Quantile
• Rank–size distribution See more

Strictly monotonic distribution function
With reference to a continuous and strictly monotonic cumulative distribution function $${\displaystyle F_{X}\colon \mathbb {R} \to [0,1]}$$ See more

Quantile functions are used in both statistical applications and Monte Carlo methods.
The quantile function … See more

The non-linear ordinary differential equation given for normal distribution is a special case of that available for any quantile function whose second derivative exists. In general the equation for a quantile, Q(p), may be given. It is See more