How can I solve an integral problem included of cumulative distribution function of chi-square distribution?

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Louis Liu
Louis Liu 2017-8-17
编辑： Louis Liu 2017-8-29
Excuse me, does anyone know how to solve an integral problem included of cumulative distribution function of chi-square distribution? For example, there is a question like the attached picture:
I want to use the int() function to solve it, however, there are two probability distribution in it, and i don't know how to deal with it.
I hope you can tell me how to solve it like using which function or method instead of giving me the correct answer. Thanks! c = 1.00, n = 100, c = 1.15, Cp = 1.12
  2 个评论
Torsten
Torsten 2017-8-17
https://de.mathworks.com/help/matlab/ref/integral.html
together with
https://de.mathworks.com/help/stats/chi2cdf.html
https://de.mathworks.com/help/stats/normpdf.html
should work.
Best wishes
Torsten.
Louis Liu
Louis Liu 2017-8-18
Hello Torsten, Actually I also find the function chi2cdf, however, when I want to use it like the attached photo,
it couldn't work. I look back the example of documentation of chi2cdf, it seems like I couldn't use eq1 variable as x in the example and then to solve the integral. Can you give me more instructions? Thanks!
@Torsten

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Torsten
Torsten 2017-8-18
fun=@(y)chi2cdf((n-1)*(3*Cp*sqrt(n)-y).^2/(9*n*cstar^2),n-1).*(normpdf(y+3*(Cp-C)*sqrt(n))+normpdf(y-3*(Cp-C)*sqrt(n)));
result=integral(fun,0,3*Cp*sqrt(n));
Of course, all the constants have to be given numerical values before calling "integral".
Don't use "syms" anywhere.
Best wishes
Torsten.
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Torsten
Torsten 2017-8-22
编辑：Torsten 2017-8-22
Try
C = 1.00;
n = 38;
alpha = 0.05;
Cp = C + 0.33;
fun = @(czero,y)chi2cdf((n-1)*(3*Cp*sqrt(n)-y).^2./(9*n*czero.^2),n-1).*(normpdf(y+3*(Cp-C)*sqrt(n))+normpdf(y-3*(Cp-C)*sqrt(n)));
czero0 = 1.0;
sol = fzero(@(czero)integral(@(y)fun(czero,y)-alpha,0,3*Cp*sqrt(n),'ArrayValued',true),czero0);
Best wishes
Torsten.

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