# 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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### Example of nonidentification mixture

Consider a continuous r.v. $X$ with pdf $f$ obeying the following finite mixture model for each $x\in \mathbb{R}$: $$f(x)=\sum_{k=1}^K \lambda_k f_k(x) \quad \lambda_k\geq 0, \sum_k\lambda_k=1$$ ...
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### How to test whether one cohort is a mixture of two other cohorts for a set of binary variables?

I'll illustrate my question with an example. Suppose I have 25 observations for 3 binary variables. The observations belong to 3 pre-labelled cohorts 1, 2, and 3. Let's say: ...
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### Is the mixture of two Gaussians with same mean also Gaussian? [duplicate]

In my problem, both random variables have zero mean, are univariate, and are independent. They may have different variances. If they happen to have the same variance, of course the mixture is Gaussian ...
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### Are discrete mixtures Gauss quadrature-like integral approximations?

I noticed that the formula for Gauss (or Newton-Cotes) quadrature looks very similar to the formula for the PDF of a general mixture distribution. Let $p_{comp}(x)$ be the PDF of a compound ...
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### Bayesian inference when distribution depends on unobserved outcome with known distribution

Let's say we have an observed outcome $Y_i$ for an object $i=1,\ldots,I$ that arises like this: For each object a coin is tossed (outcome $X_i$ = $H$ or $T$). We know the coin is fair, so \$X_i \sim \...
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Let's say I have a statistic X which is distributed as a mixture of two chi-square distributions; $$X \sim 0.5\chi^2_1 + 0.5\chi^2_2.$$ I'm wondering how I can calculate the critical value(and p-value)...