For Weibull, let \(Y=\ln(X)\). This has both scale and location parameters. Location is \(\theta_{1}=\ln(\beta)\) and scale is...
The beta distribution The parameters are \(\alpha,\beta>0\), and \(A,B\) with \(B\ge A\). \begin{equation*}...
If \(Y=\ln X\) is a normal distribution, then \(X\) is log-normal. \begin{equation*} f(x;\mu,\sigma)=\frac{1}{\sqrt{2\pi\sigma}...
Probability Density Function Let \(\alpha,\beta>0\) \begin{equation*}...
If the time between successive events is independent each with an exponential distribution with \(\lambda\), then the total time \(X\)...
Chi-squared distribution Probability Density Function The parameter is \(\nu\) and it is a positive integer. It is the gamma...
Exponential distribution Probability Density Function Let \(\lambda>0\) \begin{equation*} f(x;\lambda)=\lambda e^{-\lambda x}...
The problem with the normal distribution is that it is symmetric. The Gamma distribution is useful for skewed distributions....
Probability Distribution Function The parameters are \(-\infty<\mu<\infty\) and \(\sigma>0\). \begin{equation*}...
The Pareto distribution is good for approximating income distributions or population sizes. The pdf is given by: \begin{equation*}...
Continuous distributions are given by a probability density function (pdf): \begin{equation*} P\left(a\le X\le...