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

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Joint distribution of a mixture RV and Bernoulli RV

Let $f_Y(y)=(1-p)\frac{e^{-\lambda _0} \lambda _0^y}{y!}+p \frac{e^{-\lambda _1} \lambda _1^y}{y!}\quad $ for $y \geq 0$ be the pmf of the mixture of two poisson RVs. Let ...
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Gibbs sampling version for estimating Hierarchical Double Dirichlet Process Mixture of Gaussian Processes

I'm trying to implement Gibbs sampling to estimate the parameters of the following non-parametric model: $$\begin{align*} \beta|\gamma & \sim \text{GEM}(\gamma)\\ k_t|\beta & \sim \beta\\ ...
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A question on mixture model

I'm a bit confused by the conception of "mixtrue model" I'm studying hidden markov model, which is frequently referred to as a "mixture model". But I don't know what the term "mixture" implies. ...
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Calculating parameters for a mixture of beta distributions

I have two beta distributions with known parameters: ...
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Choice of base distribution for Dirichlet Process Mixture Model when data is categorical

While calculating a Dirichlet Process Mixture Model on a data set that has discrete/categorical attributes, what kind of base distribution would you assume? When the data set is completely numerical, ...
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31 views

Observed function of hidden random variables

Let's say a worker can perform 4 types of tasks in a day: A,B,C,D. Each of which tasks takes time that is distributed according to some probability distribution, say $$ T_A \sim Gamma(\alpha_A, ...
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Interpretation of Generalized Inverse Gaussian regression with GAMLSS

Background on my project: I am comparing proteins (nodes) between a network representing protein interactions in metastatic patients v/s another network representing protein interactions in ...
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Fitting a Gumbel mixture model in R

I am trying to fit some data to a Gumbel mixture model, however there doesn't seem to be any libraries that does this. I tried coding up my own MLE method, but am having problems. Any suggestions of ...
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60 views

Get quantile function of dynamic mixture model

I have a dynamic mixture distribution fitted to my risk data (i.e., I have all parameters) of Weibull and Generalized Pareto, with a Cauchy CDF mixing function, that can be written as: $mixture(x): ...
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can AIC be used to compare the fit of a single function and mixture model

I am trying to model a nonparametric probability density function with a continuous function or a mixture model, I am doing this with the R GAMLSS package. Given that a single function may have 4 ...
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71 views

Simulate from a dynamic mixture of distributions, honoring the tail

This question is a follow-up to this other question, brilliantly answered by Xi'an. I have a dynamic mixture of Weibull and GPD distributions (with a CDF Cauchy mixing function). The mixture is ...
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Is a gaussian mixture appropriate for TF-IDF?

I'm trying to fit multivariate mixtures of TF-IDF scaled variables. So these variables are weighted count proportions of words in a corpus (relative frequency in document weighted by the log of ...
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Simulate from a dynamic mixture of distributions

I need to sample from the following mixture of two distributions: $h_{\vec{\beta}}(r)=c(\vec{\beta})[(1-w_{m,\tau}(r))f_{\vec{\beta_{0}}}(r)+w_{m,\tau}(r)g_{\epsilon,\sigma}(r)]$ where ...
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Number of Gaussian mixture components needed to approximate any distribution

I remember reading an actual proven number of components, that can approximate any distribution. Somehow I think it was 18. Can someone point me to a book/article stating something of the sort? ...
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55 views

Degrees of freedom for chi-squared test for a random variable potentially from a mixture generation

I recently posted Multinomial mixture model but got no answer. Hence I take the liberty to present what I came up with on my own and a follow up question: I have two processes which generate a series ...
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39 views

Multinomial mixture model

Dear StackExchange Community I'm looking for a package or an elegant way to solve the following question with R: I have two processes which produce a number of A, C, G, T's following a multinomial ...
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23 views

Integrated Classification Likelihood computation for R package HDclassif

I'm in the process of fitting some mixture models to some data I have. As this data is high-dimensional, I used the subspace clustering package HDclassif. As the package has no option for the Akaike ...
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31 views

Can the mixture of two normal variables be normal?

The properties of gaussian mixtures are well known, see this post and Wikipedia. I am interested in the case when we have a linear model $$Y=a+bX+\epsilon$$ where $X$ and $\epsilon$ are normal with ...
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Finding the cumulative distribution of a mixture distribution of discrete and continuous variables

If I have a random variable that with probability 1/3 is a $U(1,2)$, with probability $1/3$ is $U(2,4)$ and with probability $1/3$ is a discrete rv that takes value 2 with probability $0.4$ and 3 with ...
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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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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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38 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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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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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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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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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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102 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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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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185 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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52 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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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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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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44 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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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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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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74 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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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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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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50 views

Density function of the mixture of two non-homogeneous Poisson processes

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 ...
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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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265 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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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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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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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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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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95 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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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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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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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 ...