# Questions tagged [mixture]

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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### Normally its easy to solving mean and covariance of Bernoulli Distribution but how we do when its Bernoulli Distribution vector in below Questions? [duplicate]

Maybe it's so easy to solve but I confused, Could anyone explain to me how can I solve these 2 questions?
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### Mixture model for a mix of normal and lognormal distributions in R

I have a distribution composed of a mixture of a normal distribution and a log-normal distribution. A simulated example that looks quite similar to what I will expect in the real data would be: ...
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### How to sample from a mixture of densities of transformed random variables?

Suppose we are given a set of $m$ random variables, $X_1$, $X_2$, ..., $X_m$, defined over the same set $\mathcal{X}$, with known densities $p_{X_i}$, for $i=1$, $2$, ..., $m$. Assume that getting ...
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### Compute mean and variance of mixture of Gaussians given mean/variance of component gaussians [duplicate]

Given $N$ means and variances $\{\mu_1,\mu_2,....\mu_N\}$ , $\{\sigma_1^2,\sigma_2^2,....\sigma_N^2 \}$ ,and the fact that combined they make a gaussian mixture, how do I compute for that mixture $M$, ...
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### Number of events in a segment if waiting times are drawn from a mixture of two exponential distributions

What is the probability for $n$ events to occur over a period of time $t$, if the duration of each individual event is $\tau_1$ with the probability $p$ and $\tau_2$ with the probability of $(1-p)$? ...
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### Extendability of finite sequences of exchangeable random variables?

The old paper Binomial Mixtures and Finite Exchangeability by G. R. Wood makes reference (see Table 2) to a 1971 conjecture of Crisma that gives a formula for the probability that an exchangeable ...
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### Convolutional roots of mixture of exponential distributions

In the reference book on infinite divisibility and generalised gamma convolution, BONDESSON, Lennart. Generalized gamma convolutions and related classes of distributions and densities. Springer ...
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### Can the likelihood ratio estimate multivariate confidence levels?

Wilks' theorem describes the log-ratio between the highest likelihood of a distribution $\mathcal{L}$ (aka the dominant mode, given at $\vec{x}_{m}$) and the likelihood of a distribution at a given ...
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### Calculation of AIC in finite mixture modeling

I have a question about calculation the AIC to find my optimal amount of clusters. I am applying mixture modeling with the EM algorithm. I know the formula AIC = -2ln(log-lik) + 2k. These are my log-...
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### mixture models in 1 d [duplicate]

I have been reading the following slides available at: http://www.inf.ed.ac.uk/teaching/courses/iaml/2011/slides/em.pdf and I found the following formula: in this part the author is trying to ...
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### Calculating the probability that an observation comes from either population A or B

If I have two normal distributions A (mean = 0, variance = 4) and B (mean = 0, variance = 16), how can I calculate the probability that an observation with magnitude 2 comes from A?
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### Why we do not accept the result of our simulation study as evidence of a limitation of one method

I am doing a mixture model. I have established a new method using EM-algorithm. I have simulated data from a mixture model. Then, I applied my new method to the data. The result is very satisfying. ...