10
$\begingroup$

The density $$f(s)\propto \frac{s}{s+\alpha}e^{-s},\quad s > 0$$ where $\alpha \ge 0$ is a parameter, lives between the exponential ($\alpha=0$) and $\Gamma(2,1)$ ($\alpha \to \infty$) distributions. Just curious if this happens to be an example of a more general family of distributions? I do not recognize it as such.

$\endgroup$
5
$\begingroup$

The density function becomes $$ f(s) = {\frac {\alpha}{1-2\,{{\rm e}^{\alpha}}{\it Ei} \left( 3,\alpha \right) }}\cdot \frac{s}{s+\alpha} e^{-s}, \quad s>0 $$ where ${\it Ei}$ is the exponential integral.

I cannot recognize that as something having a known name. Where did you encounter this?

$\endgroup$
  • 2
    $\begingroup$ I needed to define it in the course of working on problem in mathematical genetics. It would not surprise me to find that it is relatively unknown -- always good to double-check though! $\endgroup$ – jth Jul 21 at 16:53
  • 2
    $\begingroup$ This math search engine searchonmath.com/… do not find anything. $\endgroup$ – kjetil b halvorsen Jul 21 at 17:09

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.