# Questions tagged [mathematical-statistics]

Mathematical theory of statistics, concerned with formal definitions and general results.

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### Posterior distribution derivation from proportionality [duplicate]

Could someone explain to me how the proportionality is derived? What are the guidelines for terms that can/should be omitted when dealing with proportionalities to coil it into a known distribution? ...
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### Reference prior of normal distribution with unknow mean and variance

Problem: Assume that $X|\theta \sim N(\theta, \sigma^2)$ for unknow $\theta$, and unknown $\sigma$. a. Find the reference priors of $(\theta, \sigma)$, when $\sigma$ is of interest. b. Find the ...
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### Mixture random variable density

I have $X = B_1X_1 + B_2X_2 + ... + B_nX_n$ where the $X_i$ are independent random variables and the $B_i$ are independent $Bern(p_i)$ such that $\sum_{i=1}^{n} p_i =1$. I want to find the PDF and CDF ...
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### Create score from various features/variables

I have 4 measurements for different sensors and I would like to somehow create a score for each measurement ranging from 1-10. I have tried performing PCA with 1 component on these 4 columns and then ...
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### Fisher Information Matrix for Non Canonical link function for Poisson regression

I'm trying to solve this problem and I don't know how to do it since is not using the canonical link function. When I was researching online I couldn't find an example when the canonical function is ...
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