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

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Bayesian Mixture Model Gibbs Sampler for two linear relationships

I am attempting to use a Gibbs Sampler to model a mixture of two groups, where the group membership is defined by a linear relationship conditional on x. Both groups have the same slope and intercept, ...
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What is the difference between Clustering and Mixture Model Fitting

I want to know what is the difference between clustering methods and mixture model fitting. When do we use one method and when the other? How can we see or test, which method we should/can apply to ...
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Relation between sum of Gaussian RVs and Gaussian Mixture

I know that a sum of Gaussians is Gaussian. So, how is a mixture of Gaussians different? I mean, a mixture of Gaussians is just a sum of Gaussians (where each Gaussian is multiplied by the respective ...
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28 views

PMF for sum of hypergeometric distributions

Basically, my question is the same as this one, except I need more than the $k = 0$ special case: Given a sum of independent random variables each following a hypergeometric distribution, is there ...
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33 views

a perfect or symmetric bimodal distribution

I would like to know how I can measure the degree of symmetry of a bimodal distribution. Is there any a criterion like for example skewness in the case of unimodal distributions?
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1answer
30 views

Zero-inflated gamma - how to write down the cdf?

My goal is building a predictive model to give probabilistic forecasts. My response variable has lots of zeros but otherwise looks close to a gamma. I fit the whole dataset using some classification ...
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11 views

Mixture modelling to cluster populations.

I am grouping probes on a microarray that are spaced irregularly that map to different annotations. Some of these annotations appear to contain multiple populations in terms of the average probe ...
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10 views

Conditional expectation in mixture distributions

I have a mixture distribution for observed lifetime data $(\delta_i,t_i,L_i)$, where $\delta_i$ is a censoring variable (1 indicating death, and 0 indicating censoring), $t_i$ is the observed lifetime ...
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57 views

Simulate from a truncated mixture normal distribution

I want to simulate a sample from a mixture normal distribution such that $$p\times\mathcal{N}(\mu_1,\sigma_1^2) + (1-p)\times\mathcal{N}(\mu_2,\sigma_2^2) $$ is restricted to the interval $[0,1]$ ...
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38 views

Entropy of multivariate gaussian mixture random variable

Short: ${\bf X} \sim N({\bf 0},{\bf I}+{\bf I}_j)$; ${\bf I}_j\in S=\{I_j: I_j$ is diagonal and $ I_j \succeq 0\}, |S|=K$, and $j\sim U(1,K)$. What is $h({\bf X})$? What happens when ...
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1answer
114 views

Convergence from the EM Algorithm with bivariate mixture distribution

I have a mixture model which I want to find the maximum likelihood estimator of given a set of data $x$ and a set of partially observed data $z$. I have implemented both the E-step (calculating the ...
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18 views

Gibbs sampling for concentration parameter in Dirichlet Process Mixture models

Let's assume we have a DP mixture model: \begin{align} G &\sim {\rm DP}({\alpha, H})\\ \theta_i &\sim G \\ x_i &\sim F(\theta_i) \end{align} There are many methods to find the posterior ...
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22 views

Convergence of EM in Mixture Models w.r.t unlikely events $(f(\cdot)=0)$ in either distribution

To maximize the likelihood of a mixture model with unobserved latent variables, the Expectation Maximization is conventionally applied. Assuming we have data $x_1,\dots,x_n$ from a fixed number of ...
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14 views

Fit a conditional Bernoulli-gamma distribution using maximum likelihood

I am trying to model payment amounts for a collections agency. I am struggling with formulating the function I need to optimize, however. I have researched various distributions and stumbled-across ...
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1answer
34 views

Combine results from two models on a Bayesian network

I have a Bayesian Network in two versions - one where the information flows in one direction and one where all the arrows are turned around and the information flows in the other direction. After ...
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1answer
15 views

sample from a mixture

Suppose I have two types of students, male or female. Suppose a test score of a male student follows a distribution $F_m$ and suppose a test score of a female students follows a distribution $F_f$. ...
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29 views

Prediction intervals for mixture models for time series forecasting - is it really an average of the prediction intervals of the averaged models?

I'm trying to find out how to do forecasting with a mixture model (averaging the forecasts of an ets, an arima and an ...
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1answer
54 views

Where do you find info about which predictive distribution an algorithm uses for forecasting?

I am trying to fit a mixture model to a time series in order to make forecasts. I'm told that this is quite straightforward as long as the predictive distributions used by the component algorithms ...
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45 views

Distribution of the exponential of a mixture?

Suppose that $X$ is distributed as a finite mixture of normals $$\sum_{j=1}^k w_j \phi(x;\mu_j,\sigma_j^2).$$ Is $\exp(X)$ distributed as a finite mixture of log-normal distributions?
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54 views

How to compute the sum of a mixture distribution with another distribution?

I need to find the pdf of x, $f_x(x)$ which is the sum of two random variables $u$ and $w$ and they are independent. I have found the pdf but I am unsure if it is correct or not, the expression is ...
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35 views

density function of the mixture of two NHPP

I'd like to know how can I calculate the density function of the mixture of two non-homogeneous Poisson process? I should mention that I have the kernel densities of those NHPP s. I can also describe ...
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56 views

Weibull Mixture question

Is it possible that a mixture of Weibull RVs is also Weibull distributed, and if yes, what are the necessary conditions?
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228 views

Marginal Likelihood from the Gibbs Output

I'm reproducing from scratch the results in Section 4.2.1 of Marginal Likelihood from the Gibbs Output Siddhartha Chib Journal of the American Statistical Association, Vol. 90, No. 432. (Dec., ...
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1answer
31 views

Is there any repository with interval censored time-to-event datasets?

I'm looking for this particular structure of data for working on my thesis. In particular, I need interval censored with a cure fraction data. This kind is actually popular in medicine and clinical ...
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151 views

Can somebody identify this distribution?

I am searching for the name of the distribution associated with this density on $\mathbb{R}_+$: $$p(r|\lambda) = \frac{2\lambda ...
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32 views

Fitting multiple normal distributions to sample data

I have a data set of (time, action)-tuples. Actions are typically performed at approximately the same times every day, and depending on what the action is it may be done multiple times per day. If I ...
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29 views

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 ...
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61 views

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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76 views

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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63 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
38 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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34 views

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
119 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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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
54 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
254 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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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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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
45 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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182 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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79 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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65 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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220 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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82 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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100 views

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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115 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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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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128 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
128 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 ...