#Computes a single quantile for a mixture of two normal distributions.
#User must supply vector-valued mu and sigma, and scalar pi.
qmixnorm=function(p,pi,mu,sigma){
q1=qnorm(p,mu[1],sigma[1])
q2=qnorm(p,mu[2],sigma[2])
qa=min(q1,q2)
qb=max(q1,q2)
qmm=uniroot(cmm,interval=c(qa,qb),p=p,pi=pi,mu=mu,sigma=sigma)$root
qmm
}
#Computes mixed normal cdf
cmm=function(x,p,pi,mu,sigma){
cmm=pi*pnorm(x,mean=mu[1],sd=sigma[1])+
    (1-pi)*pnorm(x,mean=mu[2],sd=sigma[2])-p
cmm
}

# And some commands from class
# Example that doesn't really look like a mixture
qnorm(.7)
qnorm(.7,1,1)
x=seq(-3,4,by=.1)
par(mfrow=c(2,1))
plot(x,.5*dnorm(x)+.5*dnorm(x,1,1),type="l",xlab="f(x)")
plot(x,.5*pnorm(x)+.5*pnorm(x,1,1),type="l",xlab="F(x)")
abline(h=.7)
qmixnorm(.7,.5,c(0,1),c(1,1))
# And one that does
qnorm(.9)
qnorm(.9,3,1)
x=seq(-3,6,by=.1)
par(mfrow=c(2,1))
plot(x,.5*dnorm(x)+.5*dnorm(x,3,1),type="l",xlab="f(x)")
plot(x,.5*pnorm(x)+.5*pnorm(x,3,1),type="l",xlab="F(x)")
abline(h=.9)
qmixnorm(.9,.5,c(0,3),c(1,1))