# Questions tagged [mixing-variables]

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15 questions
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### Expressing a CDF with positive support as a mixture of two components

Consider the two-component mixture $$F(z)=\lambda F_1(z)+(1-\lambda)F_2(z)$$ where all the $F$'s are CDFs and $\lambda\in [0,1]$. A1: Assume that $F(z)=0$ $\forall z\leq 0$. Claim: A1 implies ...
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### Demonstration of an equivalence between a function a limit. [closed]

Given f(x)={0 if x is irrational and 1 if x is rational} How do I prove the following equality is true? :
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### Why are dependent (predicted) variables replicating one of the explanatory variables?

In a multiplie regression problem, I have 3 different explanatory variables X1, X2, X3 that try to explain variations in the dependent variable Y. The result (Y) is always almost the same as one of ...
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### Function needed when combining two variables

I would like some suggestions of functions to solve a problem. I need to construct a function of two variables, where the lower limit of this variables are 0 and the upper one is 100. And the ouput ...
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### Overview of the different types of mixing sequences

I have come across the terms strong mixing, $\alpha$-mixing, $\beta$-mixing, $\phi$-mixing, $\rho$-mixing. Could somebody please compile an answer that would summarize their definition in some clear ...
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### Example of a distribution that is ergodic but not $\phi$-mixing?

The book "asymptotic theory for econometricians" ststes the theory that if a stationary sequence is alpha or phi mixing, it is also ergodic, but not the other way around. However, when I look at the ...