# Tagged Questions

A mixture distribution is one that is written as a convex combination of other distributions.

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### Fitting a “pseudo” discrete dataset

I'm working with a dataset that contains information about consumption of apples. The dataset contains the amount of apple consumed in g/day. The problem with this is that the data points fall into 3 ...
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### Fitting mixture distributions and computing goodness-of-fit?

This question is a follow-up from a previous question of mine here. Thanks to @Glen_b, @gung and @rbatt for teaching me so many new things yesterday. It was mentioned in passing that mixture ...
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### Why is clutter problem intractable for large sample sizes?

Suppose we have a set of points $\mathbf{y} = \{y_1, y_2, \ldots, y_N \}$. Each point $y_i$ is generated using distribution $$p(y_i| x) = \frac12 \mathcal{N}(x, 1) + \frac12 \mathcal{N}(0, 10).$$ ...
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### How to mix probability estimators of the same phenomenon?

Also posted here and here. I have the following problem: I have N models that give me an estimation of the probability distribution function p(x) of a certain phenomenon x. Let's call them: ...
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### How to use Gaussian Mixture Models for clustering new data?

I applied Gaussian Mixture Model on my data and train the model in MATLAB. How I can test my model or use it to cluster new data? Thanks for any answer or comment.
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### Multivariate student t distribution as a mixture of distribution

I would like to derive the likelihood function corresponding to a student t model as a mixture of distribution, but there is one point which is not completely clear to me. It is usually written that ...
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### How to accomplish unsupervised separation of subpopulations?

I have a dataset drawn from a social network that looks Bimodal on logarithmic scales for all attributes (I'll demonstrate only one here): I know the variable that would give me a clean separation ...
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### Rayleigh fading from finite mixture exponential

I want to plot Rayleigh fading mixture. can any one give me help in how i can do this by matlab or R ??? this is the link of Rayleigh fading mixture : ...
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### What is the variance of the weighted mixture of two gaussians?

Say I have two normal distributions A and B with means $\mu_A$ and $\mu_B$ and variances $\sigma_A$ and $\sigma_B$. I want to take a weighted mixture of these two distributions using weights $p$ and ...
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### Approximating a binomial distribution with a mixture normal

This is purely a theoretical question (I legitimately can't think of a real application), but if you wanted to approximate a binomial distributed variable with a two-component mixture normal, is there ...
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### error of the mean in presence of background

Suppose I have a normal distribution, $N[\mu,\sigma]$, and I have a sample of size $n$. It is well know that the error (std deviation) of the mean is $\sigma/\sqrt{n}$. Now suppose that my ...
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### Visualizing results from multiple latent class models

I am using latent class analysis to cluster a sample of observations based on a set of binary variables. I am using R and the package poLCA. In LCA, you must specify the number of clusters you want to ...
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### how to show the following consistency?

It is well-known that maximum likelihood estimate for a mixture model, with the mixture distributions known, and the estimation is done for the mixture coefficients is consistent (I think) -- the ML ...
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### when is an estimator consistent?

Say there are parameters $\theta$ such that $\theta_i > 0$ and $\sum_i \theta_i = 1$ and a model such as $p(x) = \sum_{i=1}^n \theta_i p_i(x)$ where $p_i(x)$ are fixed and defined over a domain of ...
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### Inverse transformation sampling for mixture distribution of two normal distributions

I am confused by the special way required to use inverse method in the following problem, Here is the problem: Consider a mixture distribution of two normal distributions, where the desired PDF ...
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### Evaluating Gaussian PDF when det(Sigma)-->0

I want to evaluate a Gaussian PDF that does not exist because the determinant of sigma is either approx 0 or -inf (depends on parameters), and the condition number is of order 10^20. I need this ...
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### How to approximate 0 in transition probability matrix without loss of generality?

In trying to implement Mixture Markov Model, (see question here), I have extreme cases ( e.g. 0's in the Transition Probability Matrix). I have approached this with replacing 0 with 1e-17. However, I ...
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### Flipping identifiable coins in batches

I have collected data to estimate a parameter and am now puzzled about how to generate confidence intervals: Setup: 1) We have a bag with $N$ coins. 2) Each coin $i \in N$ has a known probability ...
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### Matching density with normal and uniform distributions

I will have data not too dissimilar from this: I'd like to match the density with a set of (truncated) normal distributions and one underlying uniform distribution. I know where the spikes are, ...
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### Python packages for working with Gaussian mixture models (GMMs)

There seem to be several options available for working with Gaussian Mixture Models (GMMs) in Python. At first glance there are at least: PyMix - http://www.pymix.org/pymix/index.php Tools for ...
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### Latent class model with both continuous and categorical indicators in R

I have question regarding which R-package to use to create a latent class/mixture model with both categorical and continuous indicator variables. I have not yet found a good example of this using R, ...