高校数学の質問スレ（医者・東大卒専用） Part438

588 名前：１３２人目の素数さん mailto:sage [2025/01/17(金) 18:02:26.71 ID:BcOp0/e9.net] # incubation period for COVID-19 incu=\(x){dlnorm(x,m=1.64,s=0.58) # lm=runif(1,1.6,1.8) # s=runif(1,0.4,0.6) } incu=Vectorize(incu) # window period for rapid antigen test wind=\(x) dweibull(x, shape=2.5,scale=4.5) wind=Vectorize(wind) curve(wind,0,14,col=2,xlab='days',ylab='',axes=F) ; axis(1) curve(incu,add=TRUE) legend('top',bty='n',legend=c('incubation period','window period'),lty=1:1,col=1:2) cdf_incu=\(x) integrate(incu,0,x)$value cdf_incu=Vectorize(cdf_incu) cdf_wind=\(x) integrate(wind,0,x)$value cdf_wind=Vectorize(cdf_wind) curve(cdf_wind,0,14,col=2) curve(cdf_incu,add=TRUE) legend('center',bty='n',legend=c('incubation period','window period'),lty=1:1,col=1:2) pdfZ=\(z) integrate(\(x) incu(x)*wind(x-z),0,Inf)$value pdfZ=Vectorize(pdfZ) curve(pdfZ,-10,10,xlab='incubation-window (days)',axes=F,ylab='') ; axis(1) integrate(pdfZ,-Inf,0)$value fnr=\(x) integrate(pdfZ,-Inf,-x)$value # false negative rate after x days since onset of symtom fnr=Vectorize(fnr) curve(fnr,0,7, xlab='days after onset',ylab='false negative rate') ## k=1e5 inc=rlnorm(k,m=1.64,s=0.58) win=rweibull(k,shape=2.5,scale=4.5) d=inc-win hist(d) mean(inc) mean(win) mean(inc<win) # negative test re=NULL for(i in 1:7) re=c(re,mean((inc+i)<win)) ; re plot(re,pch=16) which(re<0.05)[1]

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