library(LearnBayes)



n=seq(0,100, by = 1) 
p=dpois(n,5)
plot(n,p,type='l',main='Poisson',xlab='n',ylab='f(n,Np)',col='blue')
p=dpois(n,10)
points(n,p,type='l',col='red')
p=dpois(n,50)
points(n,p,type='l',col='green')
legend('topright',legend=c('N=5','N=10','N=50'),lty=c(1,1,1),col=c('blue','red','green'))
####
c=seq(0,10,by=0.01)
e=dexp(c,1./0.5)
plot(c,e,type='l',main='Exponential Distribution',xlab='x',ylab='f(x,xi)',col=blue)
e=dexp(c,1./2)
points(c,e,type='l',col='red')
e=dexp(c,1./4)
points(c,e,type='l',col='green')
legend('topright',legend=c('0.5','2','4'),lty=c(1,1,1),col=c('blue','red','green'))
####
n2=seq(0,20, by = 1)
b=dbinom(n2,5,0.5)
plot(n2,b,type='h',main='Binomial Distribution',xlab='n',ylab='f(n;N,p)',col='black')
b=dbinom(n2,10,0.5)
points(n2+0.1,b,type='h',col='red')

b=dbinom(n2,20,0.5)
points(n2+0.2,b,type='h',col='green')

b=dbinom(n2,20,0.8)
points(n2+0.3,b,type='h',col='blue')

b=dbinom(n2,20,0.2)
points(n2+0.4,b,type='h',col='cyan')

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
####
x3=seq(0,10,by=0.01)


l=dlnorm(x3,0,0.5)
plot(x3,l,type='l',main='Log-Normal Dist.',xlab='x',ylab='f(x;mu,sigma)')

l=dlnorm(x3,0,1)
points(x3,l,type='l',col='green')

l=dlnorm(x3,2,1)
points(x3,l,type='l',col='red')

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'))
#ToDO

x=seq(-10,10,by = 0.1)
gg=dnorm(x,2,1)

g=rnorm(100,2,1)
mu=mean(g)
med=median(g)
sig=sd(g)

hist(g,freq=FALSE,main='Random Sample',xlab='x',ylab='Prob. Density')
lines(x,gg,type='l',col='blue')

legend('topleft',legend='N = 100')
legend('topright',legend=c(med,mu,sig))
g=rnorm(1000,2,1)
mu=mean(g)
med=median(g)
sig=sd(g)


hist(g,freq=FALSE,main='Random Sample',xlab='x',ylab='Prob. Density')
lines(x,gg,type='l',col='blue')

legend('topleft',legend='N  = 1000')
legend('topright',legend=c(med,mu,sig))
#####

g=rnorm(10000,2,1)
mu=mean(g)
med=median(g)
sig=sd(g)
hist(g,freq=FALSE,main='Random Sample',xlab='x',ylab='Prob. Density')
lines(x,gg,type='l',col='blue')
legend('topleft',legend='N  = 10000')
legend('topright',legend=c(med,mu,sig))
######
# copy paste
x2=seq(-10000,10000, by = 0.1)
dn2=dnorm(x2,2,sqrt(2))
p=rpois(1000,2)
hist(p,freq=FALSE,xlab='n',ylab='Prob. Density')
lines(x2,dn2,type='l',col='blue')
legend('topright',legend=c('Np=2','Gaussian'),col=c('black','blue'),lty=c(1,1))
######

dn2=dnorm(x2,5,sqrt(5))
p=rpois(1000,5)
hist(p,freq=FALSE,xlab='n',ylab='Prob. Density')
lines(x2,dn2,type='l',col='blue')
legend('topleft',legend=c('Np=5','Gaussian'),col=c('black','blue'),lty=c(1,1))
#####

dn2=dnorm(x2,10,sqrt(10))
p=rpois(1000,10)
hist(p,freq=FALSE,main='Random Sample',xlab='n',ylab='Prob. Density')
lines(x2,dn2,type='l',col='blue')
legend('topright',legend=c('Np=10','Gaussian'),col=c('black','blue'),lty=c(1,1))
#####

dn2=dnorm(x2,100,sqrt(100))
p=rpois(1000,100)
hist(p,freq=FALSE,main='Random Sample',xlab='n',ylab='Prob. Density')
lines(x2,dn2,type='l',col='blue')
legend('topright',legend=c('Np=100','Gaussian'),col=c('black','blue'),lty=c(1,1))
####

dn2=dnorm(x2,1000,sqrt(1000))
p=rpois(1000,1000)
hist(p,freq=FALSE,main='Random Sample',xlab='n',ylab='Prob. Density')
lines(x2,dn2,type='l',col='blue')
legend('topright',legend=c('Np=1000','Gaussian'),col=c('black','blue'),lty=c(1,1))
yy = rnorm(10000,0,1)
x=seq(0,10, by = 0.1)
l = dlnorm(x,0,1)
xx=exp(yy)
hist(xx,breaks=100,freq=FALSE,main='Log-Normal Sample',xlab='x',ylab='Prob. Density',xlim=c(0,10),ylim=c(0,0.7))
lines(x,l,type='l',col='blue')

legend('topright',legend=c('exp(Random Sample)','Log-Normal Dist.'),col=c('black','blue'),lty=c(1,1))