# Questions tagged [finite-mixture-model]

Finite mixture model represents the presence of subpopulations within an overall population and describes the data in terms of mixture distribution. Finite mixture models are commonly used for model-based clustering, but they can be used also for other problems, like cluster-wise regression, mixture of generalized linear models and other mixtures. Finite mixture models for binary and categorical data are known under the name of latent class analysis.

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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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### Mixture model using mixtools package [closed]

I am trying to learn mixture models, here is the paper for the mixtools package. I tried to implement the univariate normal mixture model by myself. Below is the code: ...
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### Estimating the parameters for a true population when some of my data is spurious: can I use a mixture model?

I have a dataset where some of my data is "real" (i.e. of interest) and some is "spurious" (not of interest). I want to estimate some correlations between variables in the real ...
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### Finite Beta mixture model in stan — mixture components not identified

I'm trying to model data $0 < Y_i < 1$ with a finite mixture of Beta components. To do this, I've adapted the code given in section 5.3 of the Stan manual. Instead of (log)normal priors, I am ...
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### How to fit a statistical distribution data to a mixure of normal and lognormal distributions

I have a data set that is a mixture of one normal and one lognormal distribution. How can I fit the data to get the fit parameters? Can somebody help me with this.
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### Reversible Jump for normal mixtures in R^d

I'm reading the article "Multivariate mixtures of normals with unknown number of components" (Dellaportas and Papageorgiou 2006). In this article they describe in great details how to ...
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### What is (are) scenerios and practical settings that can possibly lead to the weibull-log-Logistic mixture distribution?

In my paper I studied Weibull-loglogistic mixture distributions in reliability and life testing, some structural properties of the model are presented including moments, reliability, hazard rate ...
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### Splitting of bimodal distribution, use in regression models

I have a bimodal length-frequency distribution for the females of a species with a one-year life span. This pattern is not observed in the males. I suspect that the bimodality is due to different ...
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### How many parameters are present in a (general) discrete mixture of five normal distributions?

What is the minimal amount of parameters that can be retained in a particular context?
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### Mixture model on binary + continuous data

If I have a dataset of continuous variables (that I can assume are normally distributed), I can identify subgroups using a Gaussian mixture model and implement. Likewise if I have binary data I can ...
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### What is the difference between the latent variable and the cluster weights in mixture models?

$p(x|\theta) = w_1 \mathcal{N}(x|\mu_1,\,\sigma_1^{2})\ + w_2 \mathcal{N}(x|\mu_2,\,\sigma_2^{2}) + w_3 \mathcal{N}(x|\mu_3,\,\sigma_3^{2})\,$ What is the difference between the the $w$ and the ...
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### Why mixture model with Gibbs sampling works?

I just have a question about why Gibbs sampling can correctly estimate parameters with random initial value? That is to say,we can sample z by: \begin{align} p(z_i=k \,|\, \cdot) &\...
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### How to latently cluster regressors based on regressors' relationship with the outcome?

What is the best way/method to model patterns across coefficients and reduce number of coefficients based on these patterns? We have hundreds of regressors on the same scale and try to reduce the ...
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### Is there a way to determine the number of the mixture components prior to run EM algorithm

I am working with mixture models. The common way to determine the number of the mixture components is fitting several mixture models with a different number of mixture components and then select the ...
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### Estimating two-component mixture of Weibull distributions?

Is there any existing package (preferably in Python or Matlab) to estimate the parameters of a two-component Weibull mixture model? And failing that, I am hoping to get some pointers towards rolling ...
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### latent variables in EM algorithm are assumed to be i.i.d from multinomial distribution, from what they are idependent

In EM algorithm we introduce a latent variables, say $z_i$, $i=1,...n$, $n$ is the number of the mixture component. These variables ($z_i$) are assumed to be independent and identically distributed ...
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### Latent profile analysis - Gaussian models and which one to choose?

When performing LPA different models are possible depending on shape, volume and orientation (Figure 1. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5096736/). Can someone, please, explain in simple ...
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### When can a finite mixture of distributions drawn from a distributional family be well-described by a distribution from the same family?

This question is motivated by a situation that we frequently encounter in economic variables. We believe that the overall distribution of some variable is well approximated by a particular ...
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### Is it acceptable in mathematical saying that the E-step is equal to posterior probability

I am studying EM-algorithm for mixture data. I read that some authors said that, the E-step is equivalent to the calculation of the posterior probability (I think this come from Bayesian rule). So, my ...
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### Equivalent way of rewriting a two-component mixture

I'm confused on the following equivalent way of rewriting a two-component mixture. Consider the two-component conditional mixture $$F(z|x)=\lambda F_1(z|x)+(1-\lambda)F_2(z|x)$$ where all the $F$'...
### A 2 component mixture is symmetric if and only if $\lambda\in \{0,1,\frac{1}{2}\}$
Consider the following mixture of two densities $$f(x)=\lambda g(x-\mu_1)+(1-\lambda)g(x-\mu_2)$$ with $\lambda\in [0,1]$, $g(\cdot)$ symmetric around zero, $\mu_1<\mu_2$. Claim: the mixture is ...