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I want to work out the quantiles of a linear combiation of chi square random variables.

Suppose $\lambda_i \in \mathbb{R}$ for all $i \in \{1,2,\cdots,n\}$ and $Z = \sum_{i = 1}^n \lambda_iX_i$ and $X_1,X_2,\cdots,X_n \stackrel{\text{iid}}{\sim} \chi^2_1$.

How can I work out the quantiles?

Taylor
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Mikkel Rev
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  • The same question about the distributions is asked and answered at https://stats.stackexchange.com/questions/2035/the-distribution-of-the-linear-combination-of-gamma-random-variables. Since "working out the quantiles" is tantamount to finding the distribution and a chi-squared distribution is a Gamma distribution, I take the other to be a duplicate of this one. – whuber Aug 20 '17 at 19:35
  • The Q is formulated as if the OP is also interested in negative $\lambda_i$, which is not covered by the linked post. – kjetil b halvorsen Aug 22 '17 at 23:42
  • @whuber anyhow, abettere duplicate is https://stats.stackexchange.com/questions/72479/general-sum-of-gamma-distributions/137318#137318 – kjetil b halvorsen Aug 23 '17 at 21:14
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    @Kjetil Thank you for pointing that out. I chose the duplicate I did because it deals with *linear combinations* rather than just sums. Nevertheless, your information is valuable and so I will include that thread within the list of duplicates. The system enables us to list up to five duplicates for any closed question, so feel free to identify more! – whuber Aug 23 '17 at 22:10

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