# Questions tagged [distributions]

A distribution is a mathematical description of probabilities or frequencies.

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### Find pdf of X+Y

Let X ∼ Exp(λ) and Y ∼ Exp(μ) be two independent exponential random variables, where λ, μ > 0. Find the probability density function of X + Y if λ ̸= μ. I have successfully find ans if λ = μ, but ...
1 vote
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### Binary Classification Problem with Predicted Probabilities distribution skewed

I have a balancedrandomforest model which was trained on unbalanced data (92/8) for a binary classification problem. The AUC is around 0.98 and the precision and recall are also acceptable being 0.89 ...
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### Betting on a sample from a known distribution

This was an interview question. Given a known distribution, sample a value from it with replacement for many times. Two people A and B bet on the sample with their own guesses, and the one closer to ...
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### "Consensus" on Analyzing Mixed Continuous and Categorical Data in the field of Statistics? [closed]

I have been trying to determine the popular "consensus" as to how mixed continuous and categorical data (e.g. a dataset that has variables on income and gender) is generally analyzed in the ...
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### How can I get an MME of negative multinomial distribution?

I know there is an MME(method of moment estimator) of negative multinomial distribution on Wikipedia (https://en.wikipedia.org/wiki/Negative_multinomial_distribution). However, the process of ...
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### how to generate data from beta-Liouville distribution?

I want to test my model following the beta liouville distribution, so as a synthetic data, I need generate data from this distribution. can anyone mathematically tell me how to calculate it? this is ...
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### Find asymptotic variance of the moment estimator

I have that $$f(x)=\frac{1}{\sqrt{2 \pi}}e^{-\frac{1}{2}x^2}$$ I have the conditional distribution: $$f_{\beta}(y|x)=\frac{1}{\sqrt{2 \pi}}e^{-\frac{1}{2}(y-\beta_0-\beta_1x-\beta_2x^2)^2}$$ and we ...
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### If Y is the sum of normalized multivariate pareto random variables then Y is a Feller-Pareto random variable

If we let $\underset{k\times 1}{\boldsymbol{X}}=(X_1, \dots, X_k)' \sim MP^{(k)}(\boldsymbol{0},\boldsymbol{1}, \alpha)$ where MP denotes a Multivariate-Pareto distribution, with joint survival ...
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### Skewed distributions: choosing the median or average

Goal: To determine whether to use the median or average (or a weighted combination of the two) from a data set based on whether ...
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### Usefulness of KS tests and other similar distribution comparing tests

I am working on a machine learning binary classification problem. I have an outcome variable status called as loan paid and <...
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### QQ Plot help meaning [duplicate]

How can I interpret the following QQ Plot? Can you explain it for example for the point 20 and 12?
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### Find the probability of which sample comes from a "higher" distribution based on random sample from two distributions

I am trying to find the answer for the following question. I have two distributions of numbers between 1 and 8, as illustrated here: I draw random samples from each distribution, which we can call &...
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### Top 10 win probabilities

I am a newbie here, hoping to find the right response for my question. I have a task at my hand to create some kind of model that can help me to determine what is the chance of winning a certain ...
1 vote
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### Methods to handle an arbitrary peak within a distribution

I had someone come to me for advice on how to deal with their weird data. The predictor variable is categorical (experimental condition), and the outcome variable is continuous (amount of money in a ...
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### Infinitesimal Robustness, influence function of $T$ at $F$

This text is taken from Introduction to robust estimation and hypothesis testing. Wilcox R. First I will write down the description that leads to definition of relative influence on $T(F)$ and then I ...
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### Fermi-Dirac Statistics and Maxwell-Boltzmann Statistics

Answer to question (b) relates to Maxwell-Boltzmann statistics. But how to show that the probability of each distinguishable distribution is $n*N^{-r} ?$ Each distinguishable distribution have equal ...
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### n-th quantile for bivariate variable

I generate a 2000 bivariate random samples which are negative correlated. I used np.quantile to generate 10 quantile from this random samples. The related point is marked in the following figure. I am ...
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### Combinations from different sets with weightings

Imagine the following scenario: I want to create 1000 unique combinations of clothing. The combinations would include the following categories: hats, shirts, shorts, socks and shoes. Each combination ...
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### Determining distribution based on first three even moments

Given that $E(X^2) = 1, E(X^4) = 3, E(X^6) = 9$, determine all possible distributions of X. I'm sure there's some insight I'm missing here. I noted that X is mesokurtic, so it's possibly normal... but ...
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1 vote
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### Describing / fitting a highly skewed distribution

I've got a data set of 84,529 entries, each entry referring to the number of times a particular entry is cited in a database. This set is extremely skewed, ranging from entries with 0 citations to one ...
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