SS2012-StatisticalMethods.git

add solutions for Problem sheet 1 and 2
Parent a7fc161
Michi

Michi commited on 2012-05-16 13:38:38
Zeige 2 geänderte Dateien mit 153 Einfügungen und 0 Löschungen.

1/solution.r
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+library(LearnBayes)
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+
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+p = seq(0.05, 0.95, by = 0.1)
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+prior = c(1,5.2,8,7.2,4.6,2.1, 0.7, 0.1, 0.0, 0.0)
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+prior = prior/sum(prior)
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+
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+
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+data = c(11,6)
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+post = pdisc(p, prior, data)
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+round(cbind(p,prior,post),2)
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+
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+par(font.lab=2)
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+par(font.axis=2)
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+plot(p, prior, type = "h", xlab='p',ylab ="probability",lwd=2, ylim=c(0,0.5),xlim=c(0,1))
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+lines(p,post, type="h",lwd=2,lty=2,col="blue")
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+
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+legend("topleft",legend=c("prior","posterior"),lty=c(1,2),lwd=c(2,2),col=c("black","blue"))
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+
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+
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+
2/solution.r
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+library(LearnBayes)
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+
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+
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+
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+n=seq(0,100, by = 1)
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+p=dpois(n,5)
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+plot(n,p,type='l',main='Poisson',xlab='n',ylab='f(n,Np)',col='blue')
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+p=dpois(n,10)
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+points(n,p,type='l',col='red')
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+p=dpois(n,50)
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+points(n,p,type='l',col='green')
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+legend('topright',legend=c('N=5','N=10','N=50'),lty=c(1,1,1),col=c('blue','red','green'))
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+####
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+c=seq(0,10,by=0.01)
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+e=dexp(c,1./0.5)
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+plot(c,e,type='l',main='Exponential Distribution',xlab='x',ylab='f(x,xi)',col=blue)
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+e=dexp(c,1./2)
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+points(c,e,type='l',col='red')
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+e=dexp(c,1./4)
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+points(c,e,type='l',col='green')
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+legend('topright',legend=c('0.5','2','4'),lty=c(1,1,1),col=c('blue','red','green'))
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+####
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+n2=seq(0,20, by = 1)
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+b=dbinom(n2,5,0.5)
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+plot(n2,b,type='h',main='Binomial Distribution',xlab='n',ylab='f(n;N,p)',col='black')
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+b=dbinom(n2,10,0.5)
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+points(n2+0.1,b,type='h',col='red')
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+
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+b=dbinom(n2,20,0.5)
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+points(n2+0.2,b,type='h',col='green')
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+
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+b=dbinom(n2,20,0.8)
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+points(n2+0.3,b,type='h',col='blue')
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+
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+b=dbinom(n2,20,0.2)
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+points(n2+0.4,b,type='h',col='cyan')
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+
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+legend('topright',legend=c('(5,0.5)','(10,0.5)','(20,0.5)','(20,0.8)','(20,0.2)'),lty=c(1,1,1,1,1),col=c('black','red','green','blue','cyan')) #To fix
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+####
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+x3=seq(0,10,by=0.01)
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+
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+
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+l=dlnorm(x3,0,0.5)
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+plot(x3,l,type='l',main='Log-Normal Dist.',xlab='x',ylab='f(x;mu,sigma)')
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+
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+l=dlnorm(x3,0,1)
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+points(x3,l,type='l',col='green')
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+
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+l=dlnorm(x3,2,1)
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+points(x3,l,type='l',col='red')
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+
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+legend('topright',legend=c('mu=0 ,sigma=0.5','mu=0 ,sigma=1','mu=2 ,sigma=1'),lty=c(1,1,1),col=c('black','green','red'))
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+#ToDO
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+
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+x=seq(-10,10,by = 0.1)
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+gg=dnorm(x,2,1)
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+
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+g=rnorm(100,2,1)
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+mu=mean(g)
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+med=median(g)
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+sig=sd(g)
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+
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+hist(g,freq=FALSE,main='Random Sample',xlab='x',ylab='Prob. Density')
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+lines(x,gg,type='l',col='blue')
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+
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+legend('topleft',legend='N = 100')
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+legend('topright',legend=c(med,mu,sig))
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+g=rnorm(1000,2,1)
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+mu=mean(g)
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+med=median(g)
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+sig=sd(g)
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+
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+
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+hist(g,freq=FALSE,main='Random Sample',xlab='x',ylab='Prob. Density')
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+lines(x,gg,type='l',col='blue')
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+
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+legend('topleft',legend='N  = 1000')
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+legend('topright',legend=c(med,mu,sig))
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+#####
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+
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+g=rnorm(10000,2,1)
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+mu=mean(g)
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+med=median(g)
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+sig=sd(g)
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+hist(g,freq=FALSE,main='Random Sample',xlab='x',ylab='Prob. Density')
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+lines(x,gg,type='l',col='blue')
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+legend('topleft',legend='N  = 10000')
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+legend('topright',legend=c(med,mu,sig))
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+######
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+# copy paste
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+x2=seq(-10000,10000, by = 0.1)
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+dn2=dnorm(x2,2,sqrt(2))
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+p=rpois(1000,2)
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+hist(p,freq=FALSE,xlab='n',ylab='Prob. Density')
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+lines(x2,dn2,type='l',col='blue')
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+legend('topright',legend=c('Np=2','Gaussian'),col=c('black','blue'),lty=c(1,1))
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+######
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+
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+dn2=dnorm(x2,5,sqrt(5))
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+p=rpois(1000,5)
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+hist(p,freq=FALSE,xlab='n',ylab='Prob. Density')
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+lines(x2,dn2,type='l',col='blue')
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+legend('topleft',legend=c('Np=5','Gaussian'),col=c('black','blue'),lty=c(1,1))
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+#####
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+
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+dn2=dnorm(x2,10,sqrt(10))
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+p=rpois(1000,10)
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+hist(p,freq=FALSE,main='Random Sample',xlab='n',ylab='Prob. Density')
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+lines(x2,dn2,type='l',col='blue')
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+legend('topright',legend=c('Np=10','Gaussian'),col=c('black','blue'),lty=c(1,1))
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+#####
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+
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+dn2=dnorm(x2,100,sqrt(100))
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+p=rpois(1000,100)
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+hist(p,freq=FALSE,main='Random Sample',xlab='n',ylab='Prob. Density')
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+lines(x2,dn2,type='l',col='blue')
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+legend('topright',legend=c('Np=100','Gaussian'),col=c('black','blue'),lty=c(1,1))
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+####
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+
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+dn2=dnorm(x2,1000,sqrt(1000))
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+p=rpois(1000,1000)
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+hist(p,freq=FALSE,main='Random Sample',xlab='n',ylab='Prob. Density')
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+lines(x2,dn2,type='l',col='blue')
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+legend('topright',legend=c('Np=1000','Gaussian'),col=c('black','blue'),lty=c(1,1))
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+yy = rnorm(10000,0,1)
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+x=seq(0,10, by = 0.1)
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+l = dlnorm(x,0,1)
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+xx=exp(yy)
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+hist(xx,breaks=100,freq=FALSE,main='Distribution of a Log-Normal Sample',xlab='x',ylab='Prob. Density',xlim=c(0,10),ylim=c(0,0.7))
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+lines(x,l,type='l',col='blue')
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+
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+legend('topright',legend=c('exp(Random Sample)','Log-Normal Dist.'),col=c('black','blue'),lty=c(1,1))
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+
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