# Questions tagged [mixture-distribution]

A mixture distribution is one that is written as a convex combination of other distributions. Use the "compound-distributions" tag for "concatenations" of distributions (where a parameter of a distribution is itself a random variable).

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### How to analyse this bimodal gamma distribution?

I have collected physiological data with multiple observations from 35 people, across four conditions. In planning the experiment, I had been hoping to perform inferential statistics comparing between ...
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### mixture of exponential and gamma distribution

I'm not particularly good at statistics and whatever elementary statistics I have had exposure to are now rusty. However, I am working on a problem that I am hoping to gain some insights into: My goal ...
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### Expected log likelihood for mixture components with differing support

I was hoping to use the EM algorithm to fit a mixture model in which the mixture components can have differing support. I've run into a problem during the M step because the expected log-likelihood ...
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### Resampling classes across weighted source distributions

I am sure this is a common problem, but googling only yielded false positives. I probably did not know what terms to search for. So here we go: I have $n$ classes from $m$ different sources. Each ...
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### Correlation and mixture

Suppose we have a mixture distribution (same parametric family) and we know that a third variable $X$ is correlated to each of those variables in the mixture with coefficients $\rho_1$, $\rho_2$, ...
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Define a linear space $X=\Delta(Z)$. $Z=\mathbb R_+$ is the real valued outcome space and $\Delta$ is a probability simplex. Let $f$ and $g$ denote the elements in $X$. Suppose now I define a mixture $... • 359 1 vote 1 answer 95 views ### Generating random variable from no closed-form marginal density [closed] Suppose$u\sim N(0,I_p)$and$Y|U\sim N(x(t),\sigma_e^2I_m)$, and the marginal distribution of$y$is$f(y)=\int_u f(y|u)f(u)du$.$x(t)$is composite function of$u$, basically$x(t)$is a function of ... • 19 1 vote 0 answers 27 views ### Generating random variable from mixture representation [duplicate] Suppose$u\sim N(0,I_p)$and$Y|U\sim N(x(t),\sigma_e^2I_m)$, and the marginal distribution of$y$is$f(y)=\int f(y|u)f(u)du$.$x(t)$is composite function of$u$. The problem is I need to generate ... • 19 5 votes 2 answers 653 views ### Metropolis Hastings algorithm bivariate normals I need some help implementing the (1) independence Gaussian proposal and (2) random walk Gaussian proposal to simulate from a mixture bivariate normal distribution. "If we have a continuous state ... • 533 6 votes 2 answers 448 views ### Negative Binomial as Gamma-Poisson Mixture or Compound Logarithmic Poisson: can this correspondence be generalized to other distributions? Preamble A random variable$X$with a negative binomial distribution can be characterized in three ways: [Negative Binomial]$X\sim\operatorname{NegBin}(r,p)$for some$r$and$p$; [Gamma-Poisson ... • 185 2 votes 0 answers 73 views ### Approximate a distribution as mixture of$K$other (known, fixed) distributions I'd like to draw samples from some "target" probability density function$f(x)$. However, I don't have a way to do that -- instead I just have access to$N$samples, each drawn from one of$...
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Let $X_1,X_2,\dotsc,X_n$ be $n$ random variables, and $X_i, i=1,\dotsc,n$ has a density function as $f_i(x)=\lambda_{i1} g_1(x)+\dotsm+\lambda_{im} g_m(x)$, where $g_j, j=1,...m$ are density functions ...