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

learn more… | top users | synonyms

2
votes
1answer
26 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 ...
1
vote
1answer
27 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.
0
votes
0answers
20 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 ...
0
votes
0answers
21 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 ...
1
vote
0answers
47 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 ...
0
votes
1answer
44 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 ...
2
votes
0answers
47 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 ...
2
votes
2answers
116 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 ...
4
votes
0answers
35 views

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 ...
1
vote
0answers
25 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. ...
1
vote
1answer
82 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 ...
1
vote
0answers
36 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 ...
1
vote
0answers
27 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 ...
0
votes
0answers
37 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 ...
0
votes
0answers
40 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 : ...
1
vote
1answer
36 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: ...
0
votes
0answers
30 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 ...
0
votes
0answers
29 views

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 ...
2
votes
0answers
64 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 ...
0
votes
1answer
113 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 ...
1
vote
0answers
45 views

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 ...
3
votes
1answer
52 views

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 ...
5
votes
3answers
985 views

Simulating random variables from a mixture of Normal distributions

How can I sample from a mixture distribution, and in particular a mixture of Normal distributions in R? For example, if I wanted to sample from: $$ ...
0
votes
0answers
58 views

Akaike criterion for gaussian mixtures

I am trying to estimate a multimodal gaussian mixture model with an unknown number of nodes. I wish to use a model selection strategy and iteratively test whether incremental modes leads to ...
2
votes
1answer
91 views

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 ...
2
votes
4answers
146 views

Can a function be split into sub-function to prove it is a probability mass function? And how to find variance of such function?

I have a question that requires to prove if the following function whether is it a PMF with poisson random variable. The function is as follows... $f(x) = \pi \frac {\lambda_1^x}{x!} e^{-\lambda_1} + ...
1
vote
1answer
72 views

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 ...
2
votes
1answer
109 views

Can log-likelihood function calculated value (M-step) be smaller after 1 EM-iteration?

I am applying a MAP log-likelihood approach in order to fit a Markov mixture model, where objective function to be maximized is given by the formula: $$ L(X|\Theta ...
3
votes
1answer
72 views

Mean and covariance of a mixture of two distributions

This is a homework problem. If I could have some hints on how to solve it that would be great. Mean and Covariance of a Mixture of Two Distributions: $$ I = \left\{ \begin{array}{l l} 1 ...
1
vote
2answers
114 views

E-step in EM-algorithm using MAP estimate (mixed Markov models), what does it calculate?

I am trying to grasp what exactly is "estimated" in the E-step of the algorithm. According to all definitions, in E-step the "conditional expectation values , or posterior probabilities of the ...
0
votes
1answer
111 views

Markov chains that do not contain all the states in the model

I am trying to understand Mixture Markov Models in order to cluster a set of sequences that do not necessarily all have the same states occurring in them. If I have several sequences that I am ...
4
votes
1answer
104 views

Multimodal data - where does one tail end and the other begin?

I have some observed (i.e., not generated by any hypothesized distribution, but generated by real processes) data that I believe is bi-modal (it may have more modes than two). In this dataset, there ...
0
votes
1answer
137 views
0
votes
1answer
90 views

Implementing EM clustering for a mixture markov model

I have a mixture Markov model (containing K clusters, or components) that I am trying to train, e.g perform clustering over a set of varying length sequences. Each component of the model is a first ...
2
votes
0answers
41 views

Estimating parameters of inifinite scale mixture from data

Suppose that I have an infinite scale mixture of zero-mean normal distributions, whose mixing distribution is gamma with parameters $\alpha$ and $\beta$. The data is thus distributed according to a ...
5
votes
3answers
178 views

Motivation of Expectation Maximization algorithm

In the EM algorithm approach we use Jensen's inequality to arrive at $$\log p(x|\theta) \geq \int \log p(z,x|\theta) p(z|x,\theta^{(k)}) dz - \int \log p(z|x,\theta) p(z|x,\theta^{(k)})dz$$ and ...
4
votes
1answer
100 views

Basic proof of mixture models

I need to proof that $X$ follows a distribution $F$ with probability $1-p$ and a distribution $G$ with probability $p$ if, and only if, its distribution function is: $(1-p)F + pG$ Can anyone give me ...
2
votes
0answers
202 views

Label Switching in WinBugs/JAGS

I am using JAGS to estimate a Dirichlet Process Mixture of Normals. The code works well and the estimated density is accurate. However, I would like to know which component each observation is ...
1
vote
1answer
142 views

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, ...
3
votes
1answer
150 views

Evaluating parametric vs non-parametric methods

I am having a hard time finding comparisons between non-parametric and parametric methods, specifically for the task of density estimation (e.g. GMM vs using Dirichlet Processes). More than ...
0
votes
0answers
144 views

How to implement mixture distributions for data in JAGS

In JAGS, how can I model the data being sampled from a mixture distribution? For example, I want an outcome to be either $0$ with probability $p$ or normal with probability $(1 - p)$. $p$ and the ...
1
vote
0answers
22 views

Correction term in variance of mixture [duplicate]

In the answer to this question, the correction term is claimed to be nonnegative: $$p_A \mu_A^2 + p_B \mu_B^2 - p_A^2 \mu_A^2 - p_B^2 \mu_B^2 - 2 p_A p_B \mu_A \mu_B \geq 0$$ where $p_A + p_B = 1$, $0 ...
1
vote
0answers
192 views

How to decide whether the distribution is unimodal or bimodal in grain size distribution?

In the examples given at this link, I am not able to decide whether the distribution is unimodal or bimodal. I think it is in between unimodal and bimodal, but I do not know if this kind of class ...
0
votes
0answers
65 views

Bias in EM estimation for a mixture of normal distributions

Are the parameter estimates for a mixture of two normal distribution using EM algorithm biased or unbiased? More specifically, if I use the EM-algorithm to obtain ML estimates of $μ_1$, $μ_2$, ...
4
votes
3answers
293 views

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 ...
2
votes
0answers
29 views

Compendium or catalog of compound distributions?

Does anyone know of a good compendium or catalog of compound distributions, or finite mixture representations of those distributions? I am trying to find out to what extent the common ...
0
votes
0answers
29 views

Constructing the generalized gamma distribution

Is there a finite mixture decomposition or representation, or a compound distribution representation, of the generalized gamma distribution? And if so, what is it? Citations welcome but not required.
0
votes
0answers
36 views

Approximating a compound distribution with a mixture: required n?

Suppose you have two continuous distributions, g(φ; θ) and f(θ; x), where φ and θ are parameter vectors of g and f, respectively, and the values of θ generated by g are all legal values for θ in f(θ; ...
4
votes
1answer
191 views

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 ...
1
vote
0answers
44 views

two component non standard mixture (normal + unknown)

I have some univariate data which might be well modeled as a two component mixture where the first component is normal with unknown mean and variance and the second is some unspecified continuous ...