1
vote
Accepted
Maximum Likelihood Estimation for Poisson Mean with Given Observations
The critical point $\hat \lambda$ satisfies
$$n - n_1 = \frac{n_2}{\lambda} + \frac{n_1 \lambda}{e^\lambda - (1 + \lambda)}$$
or equivalently,
$$e^\lambda = \frac{n_2 - (n - n_1 - n_2)\lambda - n \...
- 141k
1
vote
MLE of $\theta$ from $N(\theta+2, \theta^2)$
Your last derivation can be rearranged into a Quadratic Eunction form (See Quadratic Form, Quadratic Function):
$$ \underbrace{-n}_{a} {\theta}^{2} \underbrace{-\sum_{i} \left( {x}_{i} - 2 \right)}_{b}...
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