# Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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### On an infinite linear combination of chi-squared random variables

Question Let $Z_i\sim\chi_{(1)}^2$ be i.i.d. chi-squared random variables with 1 degree of freedom. We define: $$W_{\infty} = \sum_{k = 1}^{\infty} \frac{Z_k}{2^{k}}$$ I have interest in computing ...
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### Why can a model's SHAP values change on a new dataset?

Background I'm validating a model and as part of the process I've been calculating SHAP values for different validation datasets. I've calculated SHAP values for every sample in each dataset taken ...
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### Metrics to assess the difference between two distributions [closed]

I'd like to assess the difference between two distributions and am a bit overwhelmed by the potential amount of metrics (see result of my preliminary search below). Is there a book / review paper ...
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### How to show that the influence function of minimum density power divergence estimator with positive tuning parameter is bounded?

In the linked paper, in the influence function section, the term ${u_{\theta}(y)}{f_{\theta}(y)}^\alpha$ is directly called bounded which i do not get the explanation of? Here $\alpha > 0$ is the ...
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### What is the specific name of this distribution?

I just can’t seem to find the name of this distribution: $$\frac{e^{-x}}{(1+e^{-x}) ^2}.$$ From my understanding, it is generally applied to pandemics/epidemics. None of the statistics books that I ...
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### Closed form expression for the 2-Wasserstein distance between generalized Gaussian distributions

Essentially the title - is there a closed form expression for the 2-Wasserstein distance (aka Frechet distance, Earth Mover's distance) between two generalized Gaussian distributions? The regular ...
14 views

### Example of a system with contextual statistics [closed]

What is a system described by a set of random variables for which there are distributions over subsets of these variables which are not marginal of a distribution over all random variables at once. ...
1 vote
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### Multinomial regression for modelling change of proportional makeup

I’m reaching the limits of my statistical understanding here when it comes to model specification in BRMS. I’m a PhD student researching how different drivers of species distribution (generalised into ...
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### Distribution of a bootstrap sample from a given reference sample [duplicate]

Consider $n$ samples $X_1,X_2,..,X_n$, where each is normally distributed according to mean $\mu$ and variance $\sigma^2$. We use these samples to define our reference population. Given a bootstrap ...
1 vote
39 views

### Probability of Random variable less than a quantity containing random variable [closed]

What is the probability of the following: $P\left(Z_j>\frac{\epsilon}{a_j*R}\left(\sum^{M}_{m=j+1} ~ a_m*R*X_m+1\right)\right)$ where $Z_j$ and $X_m$ are independent and identically distributed ...
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### Calculating the cumulative distribution function and the probability density function of an interval with ratio of a shorter and longer segment

The interval $[0, 2]$ is divided into two parts by randomly marking a point in $[0, 1]$ according to the rectangular distribution. Let $X$ be the length ratio $L_1/L_2$ of the shorter segment $L_1$ to ...
1 vote
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### In a 2-arm clinical trial where ten centers recruited patients, how does one test that two distributions are statistically similar?

There are two arms in a clinical trial. If ten centers recruited subjects. How do I test in R that distribution across centers into two arms are statistically same? The distribution appears ...
45 views

### Methods for fitting a distribution to regression data

I'm hoping to find a method/algorithm/approach for fitting to a distribution to regression data. Essentially I have a problem where I have survival data with independent variables, but only cases that ...
1 vote
60 views

### How to approach problem [closed]

I have a discrete random variable f(phi) with known probabilities for each n outcomes. Phi represents the random variables m parameters. Each parameter is its own independent discrete random variable ...
1 vote
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### GLM: invalid value encountered in log special.gammaln

I've never used GLM before so I would like to have some hints on how to use it and if I'm missing any steps. My challenge: I want to know if the price of product is influenced, positively or ...
14 views

### Are there any research papers which show why Wasserstein distance is better than Jensen-Shannon/KL_div/Bhattacharya distance for specific use cases?

I am trying to find reliable research work which show why displacement based metrics such as Wasserstein distance is a better suited metric than Jensen-Shannon distance in specific use cases and for ...
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### Fitting data with a beta distribution using fitdist from fitdistrplus package in R

I have a variable x that corresponds to data from a database. I've been trying to find the best distribution to fit it and looking at the histogram I figured either a normal, weibull or logistic ...
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### distinguishing gradients of samples in semi supervised learning under mixup

I'm having trouble drawing conclusions from a specific semi supervised machine learning setting. My use case would be using mixup [Zhang2017] and label guessing similar to the mixmatch paper [...