I have this mixture of normal distribution:

$$X sim frac{1}{2}mathcal{N}(mu_{x_1}=10,,sigma_{x_1}^{2}=1)+frac{1}{2}mathcal{N}(mu_{x_2}=13,,sigma_{x_2}^{2}=1)$$

How can i compute the quantile function of this distributionin `R`

?

I have to prove this function:

`qmist2n=function(y,mu1=10,sigma1=1,pi=0.5,mu2=13,sigma2=1){`

(1 - pi) * qnorm(y, mu1, sigma1) + pi * qnorm(y, mu2, sigma2)

}#qmist2n

I'm not sure if this code is correct. Thanks for the help in advance!!

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#### Best Answer

The question has already been discussed here.

Possibly after it's been dealt with in 2011, the following canned solution has become available in `R`

:

`library(KScorrect) qmixnorm(.95, c(0,2,5,10), c(1,1,1,1), c(.5,.25,.2,.05)) `

Here, the first entry is the quantile, followed by the vector of means, standard deviations and weights (see https://rdrr.io/cran/KScorrect/man/dmixnorm.html).

The answer is as in the link:

`> qmixnorm(.95, c(0,2,5,10), c(1,1,1,1), c(.5,.25,.2,.05)) [1] 7.745521 `