[pstricks] plot of the sum of the second derivative of a gamma function

[Herbert Voss]

Am 20.10.2010 10:43, schrieb Cyrille Piatecki:

> where incidentaly $\mu$ is the mean of $F_1$ but this is not a problem  
> since it is easy to know the expectation from a Gamma distribution 
>  from its parameters.

hope, this helps. I have no idea what values the
constants may have ...

Herbert


\documentclass{article}

\usepackage{pst-plot,pst-math}

\begin{document}

\[ F^\prime_1 = \Gamma(x)^{-1}\left[\lambda_1 e^{- \lambda_1
x}(\lambda_1 x)^{(t_1-1)}\right]
\]

and
\[ F^\prime_2 = \Gamma(x)^{-1}\left[\lambda_2 e^{- \lambda_2
x}(\lambda_1 (x-\mu))^{(t_2-1)}\right]
\]

\begin{psgraph}[Dy=0.2,Dx=2](0,0)(10,1.1){7cm}{5cm}
  \psplot[plotpoints=1000,linecolor=red,linewidth=2pt]{0.1}{4}%
    [ /mu -0.5 def  /lambda1 0.5 def /lambda2 0.5 def /t2 1.5 def ]% the
constants
    {1 x GAMMA div
     lambda2 Euler lambda2 neg x mul exp mul
     lambda1 x mu sub t2 1 sub exp mul
     mul mul }
\end{psgraph}

\end{document}