# 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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### Do Mixture Models "Defy" Entropy?

Recently, I have learned about the principle of Maximum Entropy with regards to Probability Distribution (https://www.youtube.com/watch?v=2gTrsLVnp9c) - in particular, when certain "information&...
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### Entropy of Gaussian mixture when variance of one component gets larger

I want to prove or disprove the following relation of differential entropies: Conjecture: $\displaystyle h(f) \le h(g)$ where $f, g$ the density functions of Gaussian mixture models with equal ...
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### High dimensional behavior of Dirichlet Process-based clustering?

I have a problem stemming from Dirichlet Process Gaussian Mixture Models (DP-GMMs) in high dimension. I'll write this question so that no knowledge of DP-GMMs is needed. Let $D$ be the dimensionality ...
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### How to identify a mixture of poisson distribution and Gaussian distribution from the data?

Here is the distribution of the data. It seeme to me that it is a mixture of a poisson distribution at the begining of zero value and a Gaussian distribution. I also used the ...
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### Fitting truncated normal mixtures in R

I have a vector x, lower_bound < x < upper_bound. I would like to fit a truncated normal mixture distribution to ...
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### Distribution of sum of $n$ random variables with mixture of two exponential distributions

Suppose that the random variable $Y$ follows a mixture of two exponential distributions, that is $$f_Y(y) = \sum_{i=1}^{2}\pi_i f(y| \lambda_i)$$ where $\pi$ stands for ...
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### What determines performance in recoverying K in Gaussian Mixture Model?

My question is about what determines how hard it is to recover the number of components $K$ in a Gaussian mixture model (GMM), e.g. with the EM-algorithm. For simplicity, let's consider the case in ...
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### Probabilistic interpretation of sum of quantile functions

We know that the weighted sum of CDF $$F(x) = w_1 F_1(x) + w_2 F_2(x), \,\, w_1 + w_2 = 1$$ is the CDF of the mixture distribution. Is there a probabilistic interpretation for weighted sum of ...
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### Mixtures of Dirichlet multivariates or Dirichlet processes

I am exploring the properties of Dirichlet distributions and their parameters. When mixing two Dirichlet distributed random bivariates $$\mathbf{X}\equiv(X_1,X_2)\sim\text{Dir}(\alpha_1,\alpha_2)$$ ...
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### Sample size necessary to detect that a mixture distribution is an appropriate model

I am working on an assignment, but having some trouble understanding how I would answer the following: "Comment on the shape of the histogram as the sample size increases. Include a description ...
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### Mixture random variable density

I have $X = B_1X_1 + B_2X_2 + ... + B_nX_n$ where the $X_i$ are independent random variables and the $B_i$ are independent $Bern(p_i)$ such that $\sum_{i=1}^{n} p_i =1$. I want to find the PDF and CDF ...
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### Resampling classes across weighted source distributions

I am sure this is a common problem, but googling only yielded false positives. I probably did not know what terms to search for. So here we go: I have $n$ classes from $m$ different sources. Each ...
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### Correlation and mixture

Suppose we have a mixture distribution (same parametric family) and we know that a third variable $X$ is correlated to each of those variables in the mixture with coefficients $\rho_1$, $\rho_2$, ...
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### Calculating $p$ for mixture of Bernoulli distributions

I was reading this from University of Buffalo Mixture of Bernoulli lecture slides. So is the new $p_k$ or as they denote it $\mu_k$ for Bernoulli dist $k$ just the mean of all the points multiplied ...
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### Sum of random variables that follow a finite normal mixture distribution

Let $X_1,X_2,\dotsc,X_n$ be $n$ random variables, and $X_i, i=1,\dotsc,n$ has a density function as $f_i(x)=\lambda_{i1} g_1(x)+\dotsm+\lambda_{im} g_m(x)$, where $g_j, j=1,...m$ are density functions ...
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### Goodness of fit for mixture model? [closed]

I have a problem with my vector, I thought that it was a mixture of 2 skew T and I intent to use the ks.test: ...
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### Log-likelihood of a finite mixture distribution (PDF overflowing)

I'm trying to use a finite mixture of Dirichlet distributions in a project, but am encountering problems with the PDF becoming so large for input values close to 0 that it overflows to infinity (as ...
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### Mixture regression

I am wondering how to analyze and interpret something like the data shown in the figure below (the color is the log-density of the data points, which are a few hundred thousands in number). My ...
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### Difference of independent random variables that is not unimodal

This paywalled article shows that the difference of two i.i.d. random variables is unimodal and symmetric if the distribution of the random variables is unimodal. Is there a non-unimodal distribution ...
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