\(\displaystyle X \ \ \ has \ \ \ distribution \ \ \ Exp(\lambda) \ \ \ \ p(x| \lambda)=\lambda exp(-\lambda x) \ \ \ \ \ \ and \ \ \ \ \phi=Prob(X>x|\lambda) \)
compute the fisher information for phi.
I think \(\displaystyle \phi=e^{-\lambda x} \)
and therefore the \(\displaystyle p(x|\phi)=\phi\frac{\log{\phi}}{-x}, \ \ \ L(x,\phi)=\log{\phi}+\log{\frac{
\log{\phi}}{-x}} \)
then the calculation becomes too complex.
compute the fisher information for phi.
I think \(\displaystyle \phi=e^{-\lambda x} \)
and therefore the \(\displaystyle p(x|\phi)=\phi\frac{\log{\phi}}{-x}, \ \ \ L(x,\phi)=\log{\phi}+\log{\frac{
\log{\phi}}{-x}} \)
then the calculation becomes too complex.