# Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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### Online density estimation and learning

Suppose that I have a system that at each time $t_i$ produces $N$ i.i.d samples of an unknown distribution $f(x;t)$. I want to estimate the distribution in an online manner. If I had only the ...
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### What is the most fitting distribution for “how much time each day” kind of variable?

I frequently encounter variables with values restricted in a known interval but otherwise looking like being normally distributed. A typical one is, say, time spent browsing internet each day. I am ...
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### Good way to quantify difference/distance between (discrete) distributions?

I have a model that outputs sequences based on a multinomial distribution. A sequence is an ordered list of one-hot samples. Each sample has its own discrete distribution. So for instance, a sampling ...
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### How to find the best fit margins distribution to my data

I have data as follow: ...
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### Exponents in Binomial Distribution

Why do we have exponentials in equation of binomial distribution? What's the intuition of it?
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### Question on Rao-Cramer Lower Bound

A question with a solution that I don't quite get: asking for the Cramér-Rao lower bound of a random Poisson sample. If we take the log of the function $f(x; \theta)$ and take its first derivative ...
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### Consequences of choosing the wrong GLM response distribution

In Chapter 10 of McElreath's Statistical Rethinking (2nd edition), he argues that the response distribution for a GLM should be chosen to maximize entropy given a set of constraints on the response ...
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### Equality in distribution - study of a condition

Given a class $\mathcal{P}$ on a Borel measurable space $(\mathbb{R},\mathfrak{F})$. Let $q\in\mathcal{P}$ and $p\in\mathcal{P}$ denote two arbitrary density functions and suppose that the following ...
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### Probability of an event happening in a given istant

Simplified context: I'm watching traffic over a computer network. I consider "connection" as an event, which obviously can repeat many times during a period of time. I observe my network for ...
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### Ways to sample from a distribution that are more efficient than random

I am trying to sample from a known distribution (somewhat complicated in that a transformed random variable has random noise from a scale mixture of normals added to it and is then back-transformed - ...
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### Multivariate rare events

My data is something like this: I have U urns, and I have taken a bag of $n$ objects from each urn. Each urn has $N$ objects, and I have sampled $n$ with replacement. $n$ is comprised of coloured ...
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### If V=X+Y how to prove that there is no independent random variables X,Y make V a uniform distribution [duplicate]

If V=X+Y,how to prove that there is no independent random variables X,Y (with the same distribution function) make V a uniform distribution function on [0,1]
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### Finding P value from t (MATLAB)

I am not really familiar with the student’s t distribution. My problem is highlighted in picture, the variables I have obtained are ‘tj’, ‘rj’(partial correlation), N(number of data points) and k(...
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### What distribution should be used to model at least 1 “hit” in n trials where the probability of each hit is not constant for each trial?

Obviously the first things that came to mind were binomial/geometric/beta binomial distributions but these all assume probability of hits are constant. As an example to try and illustrate what I am ...
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### Estimating tail deviation from Q-Q plots

I am running experiments and for certain cases am able to find a suitable distribution for the data. However, in most cases, depending on a certain parameter, the observed vs fitted distributions have ...
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### The quantile of prob=0.05 and mean

What is the meaning of the difference between the quantile of prob=0.05 and mean for a sample form a specific distribution? In other words, I would like to understand the relationship between ...
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### Can I use the square of correlation from copula to calculate the R square (co-efficient of determination)?

I have two variables, security returns, and market returns. I want to calculate R-Squared from copula correlations. What is the possible way to calculate the R-Square from the copula of these two ...
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### Why does the predictive distribution involve no $\textit{new}$ data?

Given data $(\textbf{X,Y})$, a Gaussian Process $\textbf{F}$ that is normally distributed and weights $\textbf{W}_1$ and $\textbf{b}$ also from a distribution, how come is the following distribution \...
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### Interpretation of variance of negative log probability

Given some discrete random variable $X$ with pmf $P(X)$ the expectation of its negative log probability $H(X) = E_{X}[-log(P(X))]$ is defined as the entropy which is an important statistical quantity. ...
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### GLMM with ex-Gaussian distribution function (trial-level reaction time data)

I am trying to use GLMM in R to fit a mixed-effects model (three categorical predictors, one continuous predictor) to trial-level reaction times from a group of participants. The reaction time ...