Calculating Critical Value for Mixture of Two Chi-Square Distributions

Asked Aug 02 '22 at 19:54

Active Aug 02 '22 at 20:16

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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) for this statistic $X$ at a given significance level $\alpha$?

edited Aug 02 '22 at 20:16

Stephan Kolassa

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asked Aug 02 '22 at 19:54

Pame

1

If the dfs of your two $\chi^2$ differ by 1, you could use emdbook::dchibarsq(). Related, but no answer: Mixture of two chi-squared distributions – Stephan Kolassa Aug 02 '22 at 20:20
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The p-value is easy, but the critical value has to be computed using numerical methods. See https://stats.stackexchange.com/a/411671/919 or https://stats.stackexchange.com/a/496147/919 for the details and working general-purpose code. – whuber Aug 02 '22 at 21:14
@whuber Which method would you recommend to use to find the p-value? – Pame Aug 05 '22 at 10:16
The methods advocated in my posts on the subject: namely, use a well-crafted univariate root finder. – whuber Aug 05 '22 at 11:51

Calculating Critical Value for Mixture of Two Chi-Square Distributions

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