Timeline for Simulate from a truncated mixture normal distribution
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
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| Apr 5 at 8:01 | comment | added | Xi'an | The $\sigma_i^{-1}$ are part of the densities, not "multiplying" these densities. | |
| Apr 4 at 22:21 | comment | added | user2450223 | @Xi'an I'm talking about the sigma's in the nuerators: σ1^(−1)ϕ(σ1^(−1){x−μ1} and σ2^(−1)ϕ(σ2^(−1){x−μ2} | |
| Apr 4 at 22:15 | comment | added | user2450223 | Thanks for the reply! @Xi'an Yes, the probabilities would not add to 1. But then why have the 1/σ1 and 1/σ2 multiplying the Normal PDFs on the numerators?Am I missing the algebra? | |
| Apr 4 at 9:53 | comment | added | Xi'an | Just reflect on the fact that$$p/\sigma_1+(1-p)/\sigma_2\ne 1$$ | |
| Apr 4 at 2:32 | comment | added | user2450223 | @Xi'an Thanks for the explanation above. Shouldn't p and (1-p) be divided by σ1 and σ2 respectively. So we draw x1 with prob p/σ1 * (...) and we draw x2 with prob (1-p)/σ2 ??? | |
| Apr 4 at 2:17 | comment | added | user2450223 | @mjnichol Thanks for the explanation! Why are there the terms (σ1^−1) and (σ2^−1) in the numerators, scaling the Normal PDF densities - ϕ(σ1^−1{x−μ1}) and ϕ(σ2^−1{x−μ2}) | |
| Aug 17, 2019 at 11:38 | history | edited | Xi'an | CC BY-SA 4.0 |
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| Aug 16, 2019 at 21:10 | review | Suggested edits | |||
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| Oct 6, 2016 at 15:33 | history | edited | gung - Reinstate Monica | CC BY-SA 3.0 |
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| May 12, 2015 at 17:50 | comment | added | Xi'an | @mjnichol: in that case, you would have $$p\mathcal{N}_a^b(\mu_1,\sigma_1^2)+(1-p)\mathcal{N}_a^b(\mu_2,\sigma_2^2)$$so yes indeed this would work. | |
| May 12, 2015 at 16:52 | comment | added | mjnichol | @Xi'an: Suppose we consider a slightly different setup: What if instead of constructing the mixture distribution from weighted Gaussians and then truncating we instead mixed two already truncated Gaussians (with the same support). If the Gaussians were truncated before mixing would we be able to sample from the distribution by sampling from the first truncated Gaussian with probability p and the second with probability 1 - p? | |
| May 12, 2015 at 5:21 | comment | added | Xi'an | @mjnichol It is a mixture but with different weights than $p$ and $1-p$. | |
| May 11, 2015 at 22:03 | comment | added | mjnichol | Ah! I think I see the issue. It is because the entire distribution is being truncated, not each distribution separately. If each sub-distribution of the mixture were individually truncated before being added into the mixture then we would be able to simply sample from the distribution according to the relative weights of each sub-distribution, right? | |
| May 11, 2015 at 21:25 | comment | added | mjnichol | Why can't we just draw the sample from the first normal with probability p and the second distribution with probability 1 - p? | |
| Mar 24, 2015 at 6:18 | history | edited | Xi'an | CC BY-SA 3.0 |
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| Mar 23, 2015 at 15:33 | history | edited | Xi'an | CC BY-SA 3.0 |
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| Mar 23, 2015 at 15:31 | history | edited | Sycorax♦ | CC BY-SA 3.0 |
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| Mar 23, 2015 at 15:30 | history | answered | Xi'an | CC BY-SA 3.0 |