# Tagged Questions

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

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### variance of a mixture in terms of the mean and variance of each component

I am following the MATLAB example to fit a mixture of two normal distribution that you can find here At some point it is defined the inital guess for the standard deviation as: ...
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### RJMCMC acceptance probability of split/combine move

I have a question about the acceptance probability of Richardson & Green's RJMCMC split/combine move from their paper "On Bayesian Analysis of Mixtures with an Unknown Number of Components". In ...
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### Looking for proof of conditional dependence, when the conditioning variables are linearly related

Suppose we have three random variables, $X$, $Y_1$, and $e$ (for error). Variable $e$ is independent of $X$ and $Y_1$, but $X$ and $Y_1$ are dependent. Further suppose we construct a new mixture ...
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### Probability distribution on a subset of a simplex

I want to define a probability distribution on a subset of a simplex. for example, on a 3-simplex, we know that $x_1+x_2+x_3+x_4=1$ and $X \sim Dirichlet$. Would it be possible to constraint $X$ more (...
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### Combining monthly distributions of data with different right-censoring levels for prediction

I have a number of pricing datasets with integer values (prices in round dollars) for the same product which are right-censored at different levels (one level per dataset). I would like to combine ...
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### How to fit a mixture of quantile regressions?

I am interested in estimating a mixture of quantile regressions. I have checked several opportunities for the one-component-case as well in SAS (proc quantreg) as in R (package quantreg). But I can't ...
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### Modelling of distribution

I have faced with the following distribution (it is truncated at $0.03$ for clarity): It takes values in $(0, \infty )$, unimodal (with mode around $0.0001$), heavy-tailed, and has regular "hills". ...
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### How to combine two beta-binomial distributions

Say I have the following situation. I have two weighted coins: Coin 1: In the past I've seen this coin flipped 10 times, 8 of which it came up heads. So I can model the probability of $n$ heads out ...
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### Models for nonnegative (incl. zero) positively skewed multivariate time series (trade volumes)

I want to build a Monte Carlo simulation that is based in part on share amounts that are traded in the market for a set of stocks. I need to be able to take into account the co-dependence of trade ...
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### Tail dependence of mixture copulas

I am currently using (multivariate) mixture copulas to model a financial data set. The mixture has two components as follows: $$C_{mixture}=wC_1+(1-w)C_2$$ where $C_1$ and $C_2$ are copulas. I have ...
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### Mixture Distribution of Multiples

Is there a specific name for a mixture distribution composed of a random variable and its multiples? Suppose we start with a "atomic" random variable $A$. I want to know what one calls the ...
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### solution to mixture CDF / inverse CDF of finite mixture

I am currently numerically solving the follwing equation, which is a convex combination/finite mixture of two marginal CDFs $F(x)$ and $G(x)$ (actually they are joint CDFs but all arguments but x are ...
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### Estimate weighted variances in mixture models

Given a generic mixture model $X$ of $k$ components, with distribution $$f(x)=∑_i\pi_if_i(x),$$ It is easy to show that the $k-th$ moment is just the weighted mean of the $k-th$ moments of the ...
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### weights in a mixture Gaussian model

If the variance of a random variable is proportional to its mean, then what is the best way of making a mixture distribution that will faithfully reconstruct a data set coming from a mixture model. ...
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### Mixture of Priors/Algebra?

Can someone explain how the author gets to the expression after the words "This leads to:"
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### AIC of a mixture distribution

I'm trying to reproduce this paper: http://core.ac.uk/download/pdf/6394955.pdf where a latent class model/finite mixture model is used on the RAND Health insurance data. The data is freely available ...
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### Estimating a cumulative distribution function from a mixture model

I have a problem I fail to find a solution. Assume a mixture model : $F(x)=a\times G(x)+(1-a)\times H(x)$ where $F$, $G$ and $H$ are cumulative distributions of different random variables, and $a$ ...
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### Sampling from compartments and proportions

Let's say we now have two stacks of powders, one is $a$ the other is $b$. The ratio of amount of $a:b$ is $p:(1-p)$. The two stacks of powders are poured together (without mixing). It forms two ...
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### find peaks from response signal

My subject is to model the response of micro-organisms to the pollution of the media (one specific pollutant). We analyse the response (production of a substance) through time that is linked to the ...