# Questions tagged [statistical-inference]

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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### Computing entropy of inverse gamma distribution

I'm trying to compute the entropy of the inverse gamma distribution and it keeps coming out negative. Obviously this is wrong because entropy is always positive. Wikipedia has this derivation for the ...
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### Connection between general loss functions and the MLE

first up a big disclaimer: This question might already be answered somewhere, so if I have missed it, please just redirect me. Let $X,Y$ be two (real-valued) random variables. I will assume that their ...
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### Doubt in Convergence in Distribution . [closed]

The Limit funtion in the definition of Covergence in Distribution $$lim_{n\to\infty} F_{n}(x)=F(x)$$ It is said "F(x) or the limit funtion may or may not be Distibution function". I need the ...
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### Python implementation of type 2 error [closed]

When reading python demonstration of Data science from scratch, I encounter the following notes: ...
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### Can you use the beta-binomial distribution instead of MCMC?

So, i have a project to test the hypothesis that a marketing campaign with a new art generates more purchases than the old one, i have 2 samples of data, one using the standart ad and one using the ...
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### Computing expectation under change of random variable

I am following the work from Kingma and Welling, where they introduce Variational Autoencoders. To train such models they use the so called Evidence Lower Bound and maximize it. One way to solve this ...
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### Using differentiation under the integral sign for computing the gradient of the expectation.

I am following the work from Kingma and Welling, where they introduce Variational Autoencoders. To train such models they use the so called Evidence Lower Bound and maximize it. One way to solve this ...
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### Is it possible to design a random partition with good concentration performance?

Assume that I have n points that I wish to partition into two groups A, B. My requirement is that for each point $x_i$, the marginal distribution $P(w_i=\mathbb{1}\{x_i \in A\})=e_i$, for some pre-...
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### Prediction intervals for simple linear regression

I want to understand how to construct the test statistic for the case of predictive inference for a simple linear regression model and would be grateful if someone might confirm if my derivation is ...
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### Moments or Mean of transformed Weibull Distribution.

Given the PDF and CDF of the Weibull distribution, denoted as $f_X(x)$ and $F_X(x)$ respectively, the range is $x \geq 0$. Also, clearly that the mean, $E(x)$ would be $\int^{\infty}_{0}xf_X(x) dx$. ...
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### Logic behind hypothesis testing and one-tailed tests

Suppose I have the following: Let's consider a hypothetical experiment to determine whether James Bond can tell the difference between a shaken and a stirred martini. Suppose we gave James Bond a ...
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