probability density function
111Logistic distribution — Probability distribution name =Logistic type =density pdf cdf parameters =mu, location (real) s>0, scale (real) support =x in ( infty; +infty)! pdf =frac{e^{ (x mu)/s {sleft(1+e^{ (x mu)/s} ight)^2}! cdf =frac{1}{1+e^{ (x mu)/s! mean =mu, median …
112Von 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… …
113Chi-square distribution — Probability distribution name =chi square type =density pdf cdf parameters =k > 0, degrees of freedom support =x in [0; +infty), pdf =frac{(1/2)^{k/2{Gamma(k/2)} x^{k/2 1} e^{ x/2}, cdf =frac{gamma(k/2,x/2)}{Gamma(k/2)}, mean =k, median… …
114Lévy 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}^{… …
115Hyperbolic secant distribution — Probability distribution name =hyperbolic secant type =density pdf cdf parameters = none support =x in ( infty; +infty)! pdf =frac12 ; operatorname{sech}!left(frac{pi}{2},x ight)! cdf =frac{2}{pi} arctan!left [exp!left(frac{pi}{2},x ight) ight] ! …
116Erlang distribution — Probability distribution name =Erlang type =density pdf cdf parameters =k > 0 in mathbb{Z} shape lambda > 0, rate (real) alt.: heta = 1/lambda > 0, scale (real) support =x in [0; infty)! pdf =frac{lambda^k x^{k 1} e^{ lambda x{(k 1)!,} cdf… …
117Inverse-gamma distribution — Probability distribution name =Inverse gamma type =density pdf cdf parameters =alpha>0 shape (real) eta>0 scale (real) support =xin(0;infty)! pdf =frac{eta^alpha}{Gamma(alpha)} x^{ alpha 1} exp left(frac{ eta}{x} ight) cdf… …
118F-distribution — Probability distribution name =Fisher Snedecor type =density pdf cdf parameters =d 1>0, d 2>0 deg. of freedom support =x in [0, +infty)! pdf =frac{sqrt{frac{(d 1,x)^{d 1},,d 2^{d 2{(d 1,x+d 2)^{d 1+d 2{x,mathrm{B}!left(frac{d 1}{2},frac{d 2}{2}… …
119Wigner 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 …
120Rayleigh distribution — Probability distribution name =Rayleigh type =density pdf cdf parameters =sigma>0, support =xin [0;infty) pdf =frac{x expleft(frac{ x^2}{2sigma^2} ight)}{sigma^2} cdf =1 expleft(frac{ x^2}{2sigma^2} ight) mean =sigma sqrt{frac{pi}{2 median… …
