Mean | @f$\sqrt{\pi/2}L_{1/2}(-\nu^2/2\sigma^2)@f$ |
Variance | @f$2\sigma^2 + \nu^2 * + (\pi\sigma^2/2)L^2_{1/2}(-\nu^2/2\sigma^2)@f$ |
Range | @f$[0, \infty)@f$ |
Mean | @f$\alpha \mu / (\alpha - 1)@f$ * for @f$\alpha > 1@f$ |
Variance | @f$\alpha \mu^2 / [(\alpha - 1)^2(\alpha - 2)]@f$ * for @f$\alpha > 2@f$ |
Range | @f$[\mu, \infty)@f$ |
Mean | @f$\mu@f$ |
Variance | @f$\mu^2\frac{\lambda + \nu + 1}{\lambda\nu}@f$ |
Range | @f$[0, \infty)@f$ |
Mean | @f$ (a + b) / 2 @f$ |
Variance | @f$ (b - a)^2 / 8 @f$ |
Range | @f$[a, b]@f$ |
Mean | @f$ \sqrt{\frac{2}{\pi}} \sqrt{\frac{\omega}{1 + q^2}} * E(1 - q^2) @f$ |
Variance | @f$ \omega \left(1 - \frac{2E^2(1 - q^2)} * {\pi (1 + q^2)}\right) @f$ |
Range | @f$[0, \infty)@f$ |
Mean | @f$ \frac{a+b+c}{2} @f$ |
Variance | @f$ \frac{a^2+b^2+c^2-ab-ac-bc} * {18}@f$ |
Range | @f$[a, c]@f$ |
Mean | @f$ \mu @f$ |
Variance | @f$ 1-I_1(\kappa)/I_0(\kappa) @f$ |
Range | @f$[-\pi, \pi]@f$ |
Mean | @f$ n\frac{K}{N} @f$ |
Variance | @f$ n\frac{K}{N}\frac{N-K}{N}\frac{N-n}{N-1} * @f$ |
Range | @f$[max(0, n+K-N), min(K, n)]@f$ |
Mean | @f$a@f$ |
Variance | @f$b^2\pi^2/3@f$ |
Range | @f$[0, \infty)@f$ |