# Questions tagged [mixture-distribution]

A mixture distribution is one that is written as a convex combination of other distributions. Use the "compound-distributions" tag for "concatenations" of distributions (where a parameter of a distribution is itself a random variable).

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### mixture of exponential and gamma distribution

I'm not particularly good at statistics and whatever elementary statistics I have had exposure to are now rusty. However, I am working on a problem that I am hoping to gain some insights into: My goal ...
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### Are the subsets of Mixture Models necessarily parametrized?

Im just learning about mixture models and they are described as a "mix of parametric and non parametric models". My question is how a non-parametric subset would look like? How would e.g. EM-...
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### Expected log likelihood for mixture components with differing support

I was hoping to use the EM algorithm to fit a mixture model in which the mixture components can have differing support. I've run into a problem during the M step because the expected log-likelihood ...
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### Modeling ideas on biologics manufacturing data with complex genealogy

This question is about finding options to model the data for a biologics drug manufacturing. The manufacturing process is divided into upstream and downstream, where the output material from an ...
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### Estimating individual components of a mixture distribution

I am trying to jointly estimate the components of a mixture distribution. I have a sampling from a mixture, XY, composed of X ...
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### Bayespy model construction

I am trying to solve a classification model using a bayesian approach. In particular I am using as reference the following work: Modeling Analysts’ Recommendations via Bayesian Machine Learning The ...
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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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### Transform Copula Marginals to come from Mixture Distribution

I am trying to create a joint distribution that has a specific copula (e.g. Clayton) and whose marginals come from a mixture distribution (e.g. the mixture of two Gaussian distributions). My idea was ...
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### How to design an algorithm for k means-like problem?

I have some observation about a random variable x and I want to estimate the parameters of its probability distribution function. For example: data = {1, 2, 3, 4, 5} and choose normal distribution as ...
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### Estimating weights of known component distributions in a mixture distribution

Given $n$ probability density functions ($p_1$, ..., $p_n$) with known distributions, what are the ways of estimating the weights ($w_1$, ..., $w_n$) of these component distributions given a sample ...
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### How to sample from the distribution of the difference between two dependent mixture models

How to sample from the distribution of the difference between two dependent mixture models I have two distributions that represent a value before and after an event. Each of these distributions is ...
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### Fitting mixture model of Gaussians and uniform distributions to real data

I have times series of wind direction and velocity. For now, I leave aside the velocity and focus on the distribution of wind directions. Over there, there is usually three main wind directions, and ...
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### What is the nature of $r_i^t$?

Using Expectation Maximization (EM) algorithm, I want to vary the number of clusters used according to $K = [2,4, ... 50]$ for a normal distribution initialized randomly (...
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### How to find the Percentile of this distribution?

Let say, we have 2 IIDs $X, Y \sim N \left( 0, 1 \right) + \eta$ Now $\eta$ has a discrete distribution with values 0(-10) with probabilities 0.991 & 0.009 respectively. Also assume that $Z = X+Y$...
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### Nonparametric mixture estimation

Let's assume that we have two samples $\{X_i\}_{i=1..N}$ and $\{Y_i\}_{i=1..M}$ corresponding to random variables $X$ and $Y$. Let there also be a sample $\{Z_i\}_{i=1..K}$ corresponding to random ...
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### Method of Moments for Mixture distribution

The restaurant owner also wants to reconfigure her seating layout, and has asked you for help in modeling her clients. She gives you a dataset of past reservations, and tells you that she gets a mix ...
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### Evaluating (Uniform) Expectations over Non-simple Region

Background. Let $V = (X,Y)$ be a random vector in 2-dimensions uniformly distributed over two disjoint regions $R_X \cup R_Y$ defined as follows:  \begin{align} R_X &= ([0,1] \times [0,1]) \...
I am trying to measure the impact of a binary variable $B$ on continuous $y$, with some covariates $X$. I fit an OLS regression and a mixture model of $2$ OLS regressions. The mixture model fits much ...