# Tagged Questions

The area of statistics that focuses on taking information from samples of a population, in order to derive information on the entire population.

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### How should I calculate the MLE based on a random sample from $PAR(\theta,2)$

Consider a random sample of size $n$ from a Pareto distribution, $X_i \sim PAR(\theta, \kappa =2)$. I have to compute the MLE, $\hat \theta$, to three decimale places. So I started doing the ...
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### Necessary to find an estimator's probability distribution before calculating its expectation?

Where $X_{1}, X_{2}, \dots X_{n}$ is an iid distribution with pdf given by: \begin{cases} \frac{1}{\theta}x^{1-\theta} \qquad &\text{If $0 \leq x \leq 1$} \\[5 pt] 0 \qquad &Otherwise \end{...
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### Creating a minimal sufficient statistic with Likelihood function

To find a minimal sufficient statistic you can take the likelihood ratio and find a function $T$ so that the ratio does not depend on the parameter $\theta$ , as page 18 here http://sites.stat.psu.edu/...
Suppose $Y_{n \times 1} \sim N(X\beta,\sigma^2V)$ where $V_{n\times n}$ is invertible and $X_{n\times p}$ is of rank $p$ and $\beta_{p \times 1}$ is unknown and to be estimated by $Y$ and $X$. Which ...