# Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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### Understanding Dirichlet Distribution Variance

I need some help in understanding the variance/standard deviation in the Dirichlet distribution. I apologize in advance for the lack of latex. In the Beta distribution, as the shape parameters ...
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### Does the random variable “Number of Years” follow a Poisson probability distribution?

I am trying to figure out whether the random variable "Number of Years (since an event)" follows a common probability distribution. Specifically, I am tempted to say that it is a Poisson ...
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### How to Solve For the Inverse Cumulative Distribution Function of a Double-Exponential Probability Density Function

I'm stuck on figuring out how to sample data from a fake/known double-exponential PDF for a lab project involving C. elegans egg-laying rate data. I need help with figuring out if there's an exact ...
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### How to compare count distribution of multiple categories across months and years

I have animals counts organized into six size classes. These were taken across six months in three different years. I would like to compare the distribution of counts across size classes, between ...
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### Bootstrapping variance in R gives weird shaped distribution- how to obtain confidence intervals?

this is the first time I've used bootstrapping so it's quite basic! I'm trying to obtain confidence intervals for the standardised variance- defined as the variance over the square of the mean- across ...
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### What family of full support probability distributions satisfy that the density of any point in the domain vanishes as the variance goes to infinity?

Let $f(x,\sigma^2)$ be a representative element of a family of PDF's with full support over the reals that is indexed by their variance $\sigma^2$. Under what general conditions of the family of ...
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### X is a binomial random variable, then is aX+b follows a binomial distribution? [duplicate]

I know when X ~ N(mu, sigma^2), then aX+b follows normal distribution. But I'm curious when it happens to binomial random variable. And I don't intuitively understand how multiply constant to binomial ...
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### Peaks of estimated probability distribution are always lower than those of true distribution - why?

I have some code (shown below) for sampling from and then estimating a normal mixture distribution in one dimension. When I plot the estimate (blue) against the true distribution (black) I get images ...
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### Identical Random Variables

I am reading the book "Probability - for the enthusiastic beginner" by David Morin. The book makes the following statement about Identical random variables Xi. " The sum X1 + X2 + X3 + ....
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### Identify Poisson or Exponential Distribution and determine lambda

I am trying to identify the distribution of my variable, $X$. It measures goals per minute of soccer players. Possible values are $[0,inf]$ and they are non integers. I believe this to be an ...
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### Wilcoxon signed-rank test with large dataset and non normal distribution

While the Wilcoxon signed-rank test in general doesn't assume any distribution, most exact implementations are restricted to <50 samples (i.e. scipy). Above that a normal distribution is assumed to ...
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### Correct notation for the probability of an event in entropy

I am looking at the formula of entropy on Wikipedia, where $P(X)$ is a probability mass function. $$H(X) = -\sum_{i=1}^{n}P(x_i)log_bP(x_i)$$ I got curious why they use ...
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### Estimate parameters of a concrete categorical mixture model (information retrieval)

Let $f_{i,d}$ be the frequency of the word $i$ in the document $d$ and $l_d$ be the length of the document $d$. Then $P(X = i \mid D = d) = \frac{f_{i,d}}{l_{d}}$ is the probability of drawing the ...
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### How many neglected samples when drawn with replacement? (bagging)

I learned a while ago about an interesting place that $e$ shows up in probability: if there are $n$ items and you sample $n$ times with replacement, you would expect that the fraction of samples that ...
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### distribution of maximum random walk distance

Related to this question. Suppose I flip a fair coin $N$ times and keep track of the difference between the total number of heads and tails as I am doing it. At the end of the $N$ coin flips, I have ...
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In a probability chapter of a Python Book, there is the following problem involving a transformation of variables: I don't fully understand where the value 1/z+1 in Y > X(1/z+1) comes from, and ...
Let $F_1, F_2$ - two continuous CDF. if $F_1 = F_2\quad F_2$ almost surely (i.e. probability of $x$ where $F_1(x)\neq F_2(x)$ is zero with respect to probability with CDF $F_2$). Then $F_1 = F_2$ (...
Considering this toy example: Let $x$ be a random variable $x \sim \mathcal{N}(\mu_x, \Sigma_x)$ Where $\mu_x \in \mathbb{R}^2$ is the mean vector and $\Sigma_x \in \mathbb{R}^{2 \times 2}$ is the ...