probability density function
101Order statistic — Probability distributions for the n = 5 order statistics of an exponential distribution with θ = 3 In statistics, the kth order statistic of a statistical sample is equal to its kth smallest value. Together with rank statistics, order statistics… …
102Pareto 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… …
103Beta distribution — Probability distribution name =Beta| type =density pdf cdf parameters =alpha > 0 shape (real) eta > 0 shape (real) support =x in [0; 1] ! pdf =frac{x^{alpha 1}(1 x)^{eta 1 {mathrm{B}(alpha,eta)}! cdf =I x(alpha,eta)! mean… …
104Log-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} …
105Log-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}… …
106Weibull 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… …
107Kumaraswamy distribution — Probability distribution name =Kumaraswamy type =density pdf cdf parameters =a>0, (real)b>0, (real) support =x in [0,1] , pdf =abx^{a 1}(1 x^a)^{b 1}, cdf = [1 (1 x^a)^b] , mean =frac{bGamma(1+1/a)Gamma(b)}{Gamma(1+1/a+b)}, median =left(1… …
108Noncentral chi-square distribution — Probability distribution name =Noncentral chi square type =density pdf cdf parameters =k > 0, degrees of freedom lambda > 0, non centrality parameter support =x in [0; +infty), pdf =frac{1}{2}e^{ (x+lambda)/2}left (frac{x}{lambda} ight)^{k/4 1/2} …
109Shifted Gompertz distribution — Probability distribution name = Shifted Gompertz type =density pdf cdf parameters =b>0 scale (real) eta>0 shape (real) support =x in mathbb{R}^+ pdf =b e^{ bx} e^{ eta e^{ bxleft [1 + etaleft(1 e^{ bx} ight) ight] cdf =left(1 e^{ bx} ight)e^{ eta …
110Wishart distribution — Probability distribution name =Wishart type =density pdf cdf parameters = n > 0! deg. of freedom (real) mathbf{V} > 0, scale matrix ( pos. def) support =mathbf{W}! is positive definite pdf =frac{left|mathbf{W} ight|^frac{n p 1}{2… …
