2
votes
Accepted
Are $\mu_{\hat{p}}$ and $\sigma_{\hat{p}}$ considered parameters or statistics?
There are a variety of definitions of both, but for me a "parameter" is a value that underpins the behaviour of some random variable, while a "statistic" is a value calculated from ...
- 25.6k
2
votes
Accepted
Logic behind hypothesis testing and one-tailed tests
The key is the null hypothesis, $H_0$, which is
James Bond is guessing.
The so-called $p$-value is the probability that the evidence is at least as exceptional as what is observed, given that $H_0$ ...
- 8,679
1
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Are $\mu_{\hat{p}}$ and $\sigma_{\hat{p}}$ considered parameters or statistics?
Moments of a (parametric) distribution are parameters. That's why they are called parametric distributions. That the distribution is a sampling distribution is immaterial.
For instance, if we have ...
- 141k
1
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Measuring departure between the posterior predictive distribution and the true data generating distribution
Some random remarks:
Statistics questions, unless dealing with heavy probability theory, are probably much better directed at stats.stackexchange.com.
Your question
Suppose, I am trying to measure ...
1
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Help developing intuition behind sufficient statistics (Casella & Berger)
Suppose that the two experimenters are only "data collectors", and the "data analyst" is a different person.
Also suppose that experimenter 1 performed the experiments twice, ...
- 548
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,
$$e^\lambda = \frac{n_2 - (n - n_1 - n_2)\lambda - n \...
- 141k
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MLE of $\theta$ from $N(\theta+2, \theta^2)$
Your last derivation can be rearranged into a Quadratic Eunction form (See Quadratic Form, Quadratic Function):
$$ \underbrace{-n}_{a} {\theta}^{2} \underbrace{-\sum_{i} \left( {x}_{i} - 2 \right)}_{b}...
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