Tagged Questions

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

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Mix of two bivariate distributions (two correlations hidden in data)

We have two metric (continuous) variables, say X and Y and are interested in a correlation between X an Y. Actually, a correlation test (Pearson or Spearman) is not significant, i.e. it does not ...
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Fitting two different mixture distributions

is there a package in R to fit two different mixture distributions in R ? Let's say I want to fit a mixture of power law distribution and lognormal distribution. Is this possible ? I know you can fit ...
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Generate mixture model from data with features

I want to build a mixture model from my data, but using features of my data to calculate each component in the model. The data: For each point I have 34 associated features. Each feature is a boolean ...
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17 views

Fitting data in multivariate Gaussian

I have a dataset of N*d feature vectors and I was asked to fit them in a multivariate gaussian, with a matlab function (that someone else has programed) that recieves the number of points, mean and ...
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1answer
34 views

Is the distribution of the minimum of two other distributions a mixture distribution? Or is there a better term?

This is a terminology question motivated by a review that I got on a paper. In the following I believe that $y$ would be considered to be distributed according to a mixture distribution: $$y \sim ...
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Mixture distribution fitting for latent variable analysis

Are there any analytic approaches to using mixture distribution fitting for latent variable analysis? I'm specifically interested in existing approaches to determining whether mixture components ...
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1answer
63 views

Decompose (deconvolve) a 2-peaked pdf into 2 elementary pdfs

How could I decompose a two-peaked (empirical) pdf into 2 say lognormals or other appropriate pdf in a straightforward way? I'd prefer in Matlab. to something like this: Thanks!
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24 views

Terminology and handling of log-normal mixture distributions

The definition of a log-normal distribution of a random variable is based on normality of its logarithm. I'm curious whether there exist a specific term for cases, where log-transformed data does not ...
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1answer
32 views

Mixing probabilities in mixture models using EM

Assume we want to estimate the mixing probabilities ($\pi_{k}$) for each member distribution in the mixture model. We know that $\sum_{m}^{K}\pi_{m}=1$, so we can formulate the optimization problem ...
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1answer
42 views

EM for Mixtures of Bernoulli (M-step)

When applying the M-step for a mixture of Bernoulli distributions, one of the parameters in our maximization is the Bernoulli parameter $\mu_{k}$, where $k$ is the index of the "mixture component", ...
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3answers
43 views

Finite mixture models - Basic understanding

I have been reading lecture slides about Dirichlet Process. In page 22, there is a picture about the following finite mixture model. $$\phi _{k}\sim H\\ \pi \sim Dirichlet(\alpha /K,\dots,\alpha ...
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2answers
71 views

How can I partition a distribution into two sub-populations with fixed bias? (simulation)

I am trying to simulate a selection model for a variable $Y$ dependent on covariate vector $X$, so that two groups/sub-sets $S=(0,1)$ of observations on $Y$ are created, which have a fixed difference ...
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1answer
31 views

non-EM algorithm approach to mixture model?

I have a mixture model and the components are further parameterized by ~200 variables. Originally I use EM-algorithm to get a MLE estimation of the parameters. The algorithm works quite well and ...
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2answers
84 views

Binary version of Probabilistic Matrix Factorization in pymc?

I'm a newby in statistics, this is my first post, sorry for any possible mistake. There is a good Bayesian Probabilistic Matrix Factorization model introduced in: Bayesian Probabilistic Matrix ...
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2answers
38 views

Evaluate mixture model

I have a question concerning the evaluation of mixture models. Is there a gold standard to compute the goodness of a fit for a mixture model? What I am concerned about is how one would evaluate if ...
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0answers
42 views

How to separate distributions from weighted dataset?

I’m trying to separate two component distributions of an apparent finite mixture from a weighted dataset (determined by a weighted.histogram). I've a set of data and weights only for a part of the ...
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Restricted fitting of two-component mixture distribution in R possible?

In fitting a two-component Student's t mixture distribution to some data (standardized GARCH residuals) one of the components has an estimated degree of freedom of 0.6. This means that even the first ...
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115 views

Specifying a Normal-Log-Normal Mixture (Skew Normal) in WINBUGS/JAGS

I am an actuary working on a Bayesian loss reserve model using incremental average severity data. Exploratory analysis of the response seems to suggest a skew normal distribution of some sort would be ...
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1answer
47 views

Good (2d) visualization of a mixture model clustering

I have a specific problem which I'm surprised I don't find answers on-line and I hope somebody here has a good suggestion for me. I'm working with a large data set which I'm clustering into specific ...
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parameter estimation of a mixture distribution

I have this mixture distribution $f(x) =w \cdot \mathcal{LN}(\mu_1,\sigma) + (1-w)\cdot \mathcal{LN}(\mu_2,\sigma) $ where $\mathcal{LN}(\mu,\sigma)$ is a lognormal distribution. I now have $j$ ...
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82 views

Bernoulli mixture models for image classification, pathological cases

I'm trying to use a Bernoulli mixture model to classify MNIST images, and I'm running into pathological cases which screw up my calculations. The pdf of a multidimensional (let's say N dimensions) ...
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1answer
43 views

Identifying a mixture model

I am trying to fit a mixture model to a dataset that consists of counts (so every record is a count of something, like the number of attempts by an IP address to connect to a website). I know, a ...
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1answer
107 views

Nonparametric mixture model and clusters

I have a question about clusters that I am contemplating to treat with a nonparametric mixture approach (I think). I am working on the explanation of human comportment. Each row of my database ...
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1answer
95 views

How to test against a mixed distribution?

There is a population $D$ in which each data point has two attributes $X$ and $Y$ that are randomly distributed. While they are probably not exactly normally distributed I imagine they are not too ...
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1answer
62 views

Probability of data point being from distribution in normal mixtures

Using JMP, I was able to fit a distribution to a set of data, using the normal-2 mixtures model. It returns location (or mean), dispersion (standard deviation) and probability for each of the two ...
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1answer
106 views

Automatically fitting a mixture distribution with two univariate scaled noncentral student's t components

So far my own trials to fit such a mixture distribution to simulated or real data in R were unsuccessful (even if the data was simulated from a two-component t mixture!!!). I'm about to try the same ...
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29 views

Library for Bayesian infinite mixture models

Can anyone advise me on a good library in Python, Java or R for constructing an infinite Bayesian mixture model? Other options are also welcome. Thanks.
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25 views

Test is data is derived from mixture or just noisy normal

Is there a way to quantify \ test \ describe how likely it is that high dimensional data come from a single Gaussian or a mixture of Gaussians (with different means \ SDs) or not? What I am thinking ...
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1answer
113 views

Is there an analytic formula for the kurtosis of a (student t) mixture distribution?

The mixture distribution should be composed of noncentral scaled student t components. The mean of the mixture distribution can be calculated easily just by weighting the component means according to ...
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1answer
113 views

How fitting a mixture distribution of noncentral Student t components to a one-dimensional sample in R?

I`d like to extract the parameters of a two-component mixture distribution of noncentral student t distributions which first has to be fitted to a one-dimensional sample. My question is closely ...
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32 views

Is this method for mixing doubly Truncated Normal distribution acceptable?

Say I have to mix n double Truncated Normal distributions $\textit{TNormal(μ,σ$^{2}$,0,1)}$. Furthermore, each distribution has a weight w. w represents the influence of the distribution in the ...
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1answer
71 views

Bayesian mixture model for univariate continuous random variable

I'm quite new to the mixture models and I hope you'll help me to understand how they work. Suppose I have a univariate continuous random variable x which represents time of a visit, and suppose that ...
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1answer
31 views

What is a mixing process?

What does this mean? Asset prices follow a mixture of normal distributions with a mixing process dependent on the unobservable information arrival process.
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0answers
38 views

Is there other types of mixture distribution besides the normal mixture

There are quite a lot of study on the normal mixture distributions, say, $X=Y*Z$,where $Z$ is a normal r.v. and Y is a r.v. follows other distributions and $Y$ and $Z$ are independent. Some well-known ...
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104 views

Inverse CDF of Mixture of Gaussians Without Sampling

It is fairly straightforward to compute the inverse cdf a gaussian mixture model by doing sampling (first selecting a component of the mixture according to the coefficient of the component, then ...
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106 views

Negative binomial distribution mixture model with R

I have two data vectors of observed count data: $A$ and $B$, where count $A_n$ and $B_n$ refer to the same observation point. $A$ is assumed to follow a negative binomial distribution. $B$ is assumed ...
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1answer
131 views

Parameter Estimation of a Poisson mixture model

I want to estimate the parameters for a Poisson mixture model with 2 (and later 3) Poisson distributions. I want to use Matlab and have numerical problems to solve the loglikelihood of the mixture ...
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0answers
61 views

Separating mixture with little a priori knowledge

I have a dataset (time series data) of measured signal power values from a radio receiver. The data does not originate from a controlled experiment. I have limited knowledge of the underlying ...
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2answers
620 views

Manually fitting a mixture distribution in matlab

I am trying to fit a mixture model containing a gamma and an exponential distribution: The general form, using the pdfs, is: p * gammapdf + (1-p) * exponentialpdf. The pdfs for the Gamma and ...
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Ranking undergrad students by their future income - Mixture distribution

I would be very grateful for some advice on how to model mixture distributions with R. Given a problem to create a ranking of graduate students by their yearly income after completing their ...
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34 views

Single-class vs two-classes hypothesis testing

Consider a Gaussian mixture model of unknown parameters, having just one or two components. I would like to design a statistical test to decide the number of classes ($H_0$: single component model vs. ...
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0answers
156 views

Dirichlet process mixture model with Bayesian hierarchical clustering

I am doing Bayesian hierarchical clustering. From my understanding, there are three basic points for this algorithm. Use marginal likelihoods to decide which clusters to merge Asks what the ...
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43 views

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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35 views

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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0answers
50 views

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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0answers
43 views

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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1answer
39 views

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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0answers
32 views

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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0answers
80 views

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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1answer
158 views

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 ...