inverse distribution function
51Lévy 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}^{… …
52Characteristic function (probability theory) — The characteristic function of a uniform U(–1,1) random variable. This function is real valued because it corresponds to a random variable that is symmetric around the origin; however in general case characteristic functions may be complex valued …
53Log-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} …
54Moment-generating function — In probability theory and statistics, the moment generating function of any random variable is an alternative definition of its probability distribution. Thus, it provides the basis of an alternative route to analytical results compared with… …
55Chi-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… …
56Logistic 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 …
57Erlang 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… …
58Von 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… …
59Tukey lambda distribution — Formalized by John Tukey, the Tukey lambda distribution is a continuous probability distribution defined in terms of its quantile function. It is typically used to identify an appropriate distribution (see the comments below) and not used in… …
60Cantor function — In mathematics, the Cantor function, named after Georg Cantor, is an example of a function that is continuous, but not absolutely continuous. DefinitionThe Cantor function c : [0,1] → [0,1] is defined as follows:#Express x in base 3. If possible …
