probability moment
31Zeta distribution — Probability distribution name =zeta type =mass pdf Plot of the Zeta PMF on a log log scale. (Note that the function is only defined at integer values of k. The connecting lines do not indicate continuity.) cdf parameters =sin(1,infty) support =k… …
32Lévy distribution — Probability distribution name =Lévy (unshifted) type =density pdf cdf parameters =c > 0, support =x in [0, infty) pdf =sqrt{frac{c}{2pi frac{e^{ c/2x{x^{3/2 cdf = extrm{erfc}left(sqrt{c/2x} ight) mean =infinite median =c/2( extrm{erf}^{… …
33Wigner semicircle distribution — Probability distribution name =Wigner semicircle type =density pdf | cdf parameters =R>0! radius (real) support =x in [ R;+R] ! pdf =frac2{pi R^2},sqrt{R^2 x^2}! cdf =frac12+frac{xsqrt{R^2 x^2{pi R^2} + frac{arcsin!left(frac{x}{R} ight)}{pi}! for …
34Log-normal distribution — Probability distribution name =Log normal type =density pdf μ=0 cdf μ=0 parameters =sigma > 0 infty < mu < infty support = [0,+infty)! pdf =frac{1}{xsigmasqrt{2piexpleft [ frac{left(ln(x) mu ight)^2}{2sigma^2} ight] cdf =frac{1}{2}+frac{1}{2}… …
35Pareto distribution — Probability distribution name =Pareto type =density pdf cdf Pareto cumulative distribution functions for various k with x m = 1. The horizontal axis is the x parameter. parameters =x mathrm{m}>0, scale (real) k>0, shape (real) support =x in [x… …
36Cantor distribution — Probability distribution name =Cantor type =mass pdf cdf parameters =none support =Cantor set pdf =none cdf =Cantor function mean =1/2 median =anywhere in [1/3, 2/3] mode =n/a variance =1/8 skewness =0 kurtosis = 8/5 entropy = mgf =e^{t/2} prod… …
37Log-logistic distribution — Probability distribution name =Log logistic type =density pdf cdf parameters =alpha>0 scale eta> 0 shape support =xin [0,infty) pdf = frac{ (eta/alpha)(x/alpha)^{eta 1} } { left [ 1+(x/alpha)^{eta} ight] ^2 } cdf ={ 1 over 1+(x/alpha)^{ eta} …
38Skellam distribution — Probability distribution name =Skellam type =mass pdf Examples of the probability mass function for the Skellam distribution. The horizontal axis is the index k . (Note that the function is only defined at integer values of k . The connecting… …
39Weibull distribution — Probability distribution name =Weibull (2 Parameter) type =density pdf cdf parameters =lambda>0, scale (real) k>0, shape (real) support =x in [0; +infty), pdf =f(x)=egin{cases}frac{k}{lambda}left(frac{x}{lambda} ight)^{k 1}e^{ (x/lambda)^{k… …
40Von Mises distribution — Probability distribution name =von Mises type =density pdf The support is chosen to be [ π,π] with μ=0 cdf The support is chosen to be [ π,π] with μ=0 parameters =mu real kappa>0 support =xin any interval of length 2π pdf =frac{e^{kappacos(x… …
