We are trying to generate data points which follow "Tweedie exponential dispersion process(TED)". Here we are giving approximated PDF of TED process, which is expressed as
$f(y)=\sqrt{\frac{\lambda}{2\pi t^{1-\rho y^\rho}}}exp\{-\frac{\lambda t d(y)}{2}\}$ where $ \[ d(y) = \left \{ \begin{array}{ll} (\frac{y}{t}-\eta)^2 & \mbox{ if } \rho=0\\ 2\{\frac{y}{t}ln(\frac{y}{\eta t})-(\frac{y}{t}-\eta)\} & \mbox{ if } \rho=1\\ 2\{ln(\frac{\eta t}{y})+\frac{y}{\eta t}-1\} & \mbox{ if } \rho=2 \\ 2\{\frac{(max(\frac{y}{t},0))^{2-\rho}}{(1-\rho)(2-\rho)}-\frac{\eta^{1-\rho}y}{(1-\rho)t}+\frac{\eta^{2-\rho}}{2-\rho}\} & \mbox{ if }\rho\neq 0,1,2 \end{array} \right. \]$
see "Optimal design of step-stress accelerated degradation test oriented by nonlinear and distributed degradation process"
