# Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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### Distribution of team sizes when splitting up a company at random

A monopoly has just lost an anti-trust case with the government, and will soon be broken into two smaller, separate companies. The former owners, bitter about this outcome, withhold the organisation's ...
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### How to find the equal-weight mixture of an infinite set of probability distribution?

For example, the equal weight mixture of $p,q$ is $0.5p+0.5q$ Let $\Delta$ denote the convex hull. CASE1: The equal-weight mixture of the infinite set $\Delta(p,q)$ should be also $0.5p+0.5q$ CASE2: ...
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### Expected deviation between a theoretical discrete probability distribution and the simulated one resulting from a number of trials

Suppose we have seven colors, each associated with a theoretical probability to choose one of them. The probabilities are as follows: red ______ 0.304761904761905 blue _____ 0.304761904761905 yellow ...
1 vote
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### Statistics Inference Question: "Prob(An equation) = 1" compared with "The equation holds" [duplicate]

When I study the textbook Statistical Inference by Casella and Berger, I have often seen expressions in the form of P(an equation) = 1. However, some other textbooks or lecture notes will instead say &...
1 vote
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### Is there a known distribution for event familiarity/novelty as a function of time?

As we go through life, we see fewer and fewer things for the first time. As time goes on, the events we encounter more often resemble events we've come across before. Picture a world where we somehow ...
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### Mean of probability distributions? [duplicate]

Mean of a random variable $X$ is its expectation. I am interest in the new definition, mean of probability distributions Let $p,q$ be probability density distributions. $0.5p+0.5q$ is the mean ...
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### Comparing distribution of a biomarker among patients with overlapping clinical features

I have a question how to compare the distribution of one tested biomarker among patients with different overlapping clinical syndromes. In my case, I am investigating patients with multiple sclerosis ...
1 vote
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### Solving equations where unknown parameters are distributions

Let $\mathcal{D}_1$, $\mathcal{D}_2$ and $\mathcal{D}_3$ be three distributions defined on some space $\mathcal{X}$. Assume $\mathcal{D}_1 = \mathcal{D}_2 + \mathcal{D}_3$ and $\mathcal{D}_1$ is ...
1 vote
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### What is the probability of group cohesion while admitting people into a nightclub at random?

A crowd of size $N$ outside a club is made up of $N/G$ groups of friends, for argument's sake, e.g. $G = 5$. This is a fictitious setup… groups are usually differing in size outside nightclubs… but ...
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### How can I do valid tests simplification of a many-parameter distribution by consecutive parameter restrictions?

Suppose I have a data set that I believe is well-described as draws from a particular four- or five-parameter distribution, such as the Amaroso or the GB2. Some of those parameters can be made to ...
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### What is the probability of selecting couples from a waiting room?

Given a waiting room, filled with $N / 2$ couples ($N$ an even number: the total number of people present in the waiting room), a doctor calls $n$ individuals from the waiting room at random. What is ...
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### Can i have a distribution that is not a marginal of another distribution?

Can there be a distribution that cannot be expressed as a marginal of some other distribution?
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### Does this type of distribution have a name?

I have some integer data, produced by slightly convoluted numerical procedure, which is distributed between $0$ and $300$, with the most probable values being $0$ and $300$, and the least probable ...
1 vote
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### How to identify popular items in time-series data

I have a dataset which contains time-series events in which each event is an item chosen from a unknowably large set of items. For example, let's say that the data entries are each music playlist ...
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### Determine the distribution of a random variable

I want to solve the following A salesman has two different stores where he sells computers. The probability that he sells, in one day, a computer in the first store is $0.4$ and independently, the ...
1 vote
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### What's the best clustering algorithm for Fraud Data?

Background I'm working on a Fraud dataset with 500,000 samples, and 130 features. There are: 98 numerical features, 32 categorical features, There are missing values in: 7 numerical features, 12 ...
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### Approximating the distribution of the product of iid beta variates

Background I am interested in the distribution of $$\theta_0=1-\prod_{i=1}^n(1-\theta_i)$$ where the $\theta_{i>0}$ are iid beta random variates: $$\theta_{i>0}\sim\text{Beta}(\alpha,\beta)$$ In ...
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### How to measure the difference between two distributions of the same family?

Kullback-Leibler divergence seems to be a frequently used "metric" to measure the difference between probability distributions, regardless of their respective families. However, I would like ...
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### Representation by Poisson transform

In physics papers that dealing with multiplicity distributions in high energy collisions, I have met with that some probability distributions can be expressed as a Poisson transform. See, eg., ...
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### Hypothesis Testing - Varying p-value issue in my MWU

I have two machines (A & B) in our production line. A is older, B is very new. Both perform the same tasks, except that machine B is advanced and will perform 1 task less than the no of tasks in ...
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### Is this the formula for the conditional covariance of normally distributed random variables? [duplicate]

Assuming $X$, $Y$, and $Z$ are normally distributed random variables, is it true that: $Cov[X, Y | Z] = Cov[X, Y] - Cov[X, Z]Cov[Y, Z] / Var[Z]$ Could you provide a simple derivation?
Let $f_1$, $f_2$ be two discrete probability distributions. By Pinsker's inequality, the Kullback-Leibler divergence $D(f_1||f_2)$ sets an upper bound on the total variation distance between the two ...