# Poisson
## Probability mass function
$$
p^m(x \mid \lambda) = \frac{\lambda^x}{x!}\exp(-\lambda)
$$
$$
\log{p^m(x \mid \lambda)} = x \log{\lambda} - \log{x!} - \lambda
$$
## Diff x
離散確率分布は value による微分不可
## Diff lambda
$$
\frac{\partial \log{p^m(x \mid \lambda)}}{\partial \lambda} = \frac{x}{\lambda} - 1
$$