这是一份psu宾夕法尼亚州立大学 STAT 504作业代写的成功案
$$
f(y ; \theta)=\exp [y \theta-b(\theta)+c(y)]
$$
the conjugate distribution for the random parameter is
$$
p(\theta ; \zeta, \gamma)=\exp [\zeta \theta-\gamma b(\theta)+s(\zeta, \gamma)]
$$
where $s(\zeta, \gamma)$ is a term not involving $\theta$. This conjugate is also a member of the exponential family. The resulting compound distribution, for $n$ observations, is
$$
f(y ; \zeta, \gamma)=\exp [s(\zeta, \gamma)+c(y)-s(\zeta+y, \gamma+n)]
$$
This is not generally a member of the exponential family.
STAT 504 COURSE NOTES ：
$$
y=K \frac{\alpha \mathrm{e}^{\beta t}}{1+\alpha \mathrm{e}^{\beta t}}
$$
where $K$ is the asymptotic maximum value of the response.
We can transform this to a linear structure by using a logit link:
$$
\log \left(\frac{y}{K-y}\right)=\log (\alpha)+\beta t
$$