Benktander type I distribution

name =Benktander distribution of the first kind| type =density| pdf_image = | cdf_image = | parameters =a0 (real) 0 (real) | support =x\geq 1 | pdf = \left(\left[\left(1+\frac{2b\log x}{a}\right)\left(1+a+2b\log x\right)\right]-\frac{2b}{a}\right)x^{-\left(2+a+b\log x\right)} | cdf = 1 - \left(1+\frac{2b\log x}{a}\right)x^{-\left(a + 1 + b\log x\right)} | mean =1+\tfrac{1}{a}| median =| mode =| variance = \frac{-\sqrt{b}+ae^{\frac{(a-1)^2}{4b}}\sqrt{\pi};\textrm{erfc}\left(\frac{a-1}{2\sqrt{b}}\right)}{a^2\sqrt{b}}From Wolfram Alpha | skewness =| kurtosis =| entropy =| mgf =| char =|

The Benktander type I distribution is one of two distributions introduced by Gunnar to model heavy-tailed losses commonly found in non-life/casualty actuarial science, using various forms of mean excess functions . The distribution of the first type is "close" to the log-normal distribution .