%
% Chi-square test
% 
% Deigma n=120 zapi eivai amepolnpto

par<-c(26,13,21,29,20,11)
th<-rep(1/6,6)
th<-th*sum(par)
(par-th)^2/th
x2<-sum((par-th)^2/th)
k<-length(par)
round(c(x2,k-1,1-pchisq(x2,k-1)),4)

%
% Chi-square test
% 
% omoigeveia tessapwv pln8usmwv

agopia<-c(32,43,16,9)
n<-c(87,108,80,25)
prop.test(agopia,n)

rbind(agopia,n-agopia)
chisq.test(rbind(agopia,n-agopia))

%
% Chi-square test
% 
% elegxos kalns prosapmogns

par<-c(10,31,40,20,10,4,6)
k<-length(par)
x<-0:(k-1)
x
n<-sum(par)
n
m<-sum(par*x/n)
m
m<-2
th<-dpois(x,m)
th
th[k]<-1-sum(th[1:(k-1)])
th<-th*n
th
(par-th)^2/th
x2<-sum((par-th)^2/th)
round(c(x2,k-1,1-pchisq(x2,k-1)),4)

y<-rep(x,par)
chisq.gof(y,dist="poisson",lambda=2)
cut1<-0:k-0.1
chisq.gof(y,cut.points=cut1,dist="poisson",lambda=2)
cut1<-c(0:(k-2),k)-0.1
chisq.gof(y,cut.points=cut1,dist="poisson",lambda=2)

%
% Chi-square test
% 
% Deigma n=16 U(0,1)

set.seed(10)
x<-runif(16)
x
x<-c(0.03292479, 0.90425688, 0.53824256, 0.56344664, 0.96562332, 0.75159740, 0.70403885, 0.73285125,
     0.85374230, 0.39210198, 0.84234411, 0.64437900, 0.47865900, 0.11406144, 0.38779575, 0.65575953)

hist(x)

x.chi1<-chisq.gof(x,dist="uniform")
x.chi1
x.chi1$c
x.chi1$e
ceiling(2*16^(2/5))
x.chi1$s
x.chi1$par
x.chi1$p.


(x.chi1$c-x.chi1$e)^2/x.chi1$e
sum((x.chi1$c-x.chi1$e)^2/x.chi1$e)
x.chi1$s
1-pchisq(sum((x.chi1$c-x.chi1$e)^2/x.chi1$e),6)
x.chi1$p.


x.chi1<-chisq.gof(x,n.classes=3,dist="uniform")
x.chi1
x.chi1$c
x.chi1$e

x<-runif(50)
chisq.gof(x,dist="uniform")
chisq.gof(x,dist="uniform",min=0,max=1.5)

%
% Chi-square test
% 
% Deigma n=50 N(0,1)

x<-rnorm(50)
x

chisq.gof(x,dist="norm")
chisq.gof(x,dist="norm",mean=0,sd=1)
chisq.gof(x,dist="norm",mean=1/3,sd=1/3)
chisq.gof(x,dist="norm",n.param.est=2)
chisq.gof(x,dist="norm",n.param.est=2,mean=mean(x),sd=sqrt(var(x)))
mean(x)
var(x)


y<-rexp(60,3)

y
summary(y)

par(mfrow=c(1,2))
hist(x) 
hist(y)
 
cdf.compare(x,distr="norm")
cdf.compare(x,distr="norm",mean=mean(x),sd=sqrt(var(x)))

mean(x)
var(x)
cdf.compare(y,distr="norm",mean=mean(y),sd=sqrt(var(y)))
cdf.compare(x,y)

cdf.compare(y,distr="exp",rate=3)
qqnorm(y)
qqline(y)
qqnorm(x)
qqline(x)


chisq.gof(y,dist="norm",mean=1/3,sd=1/3)
chisq.gof(y,dist="norm",mean=0,sd=1)

chisq.gof(x,dist="norm")
chisq.gof(x,dist="norm",mean=0,sd=1)
chisq.gof(x,dist="norm",mean=1/3,sd=1/3)
chisq.gof(x,dist="norm",n.param.est=2)
chisq.gof(x,dist="norm",n.param.est=2,mean=mean(x),sd=sqrt(var(x)))
mean(x)
var(x)

x.chi1<-chisq.gof(x,dist="norm")
x.chi1$c
x.chi1$e

x.chi1<-chisq.gof(x,dist="norm",n.param.est=2)
x.chi1$c
x.chi1$e

cut1<-(-3:3)
cut1
x.chi1<-chisq.gof(x,cut.points=cut1,dist="norm")
x.chi1
x.chi1$c
x.chi1$e

cut3<-c(min(x)-0.1,seq(-1.5,1.5,by=.5),max(x)+0.1)
cut3
x.chi3<-chisq.gof(x,cut.points=cut3,dist="norm")
x.chi3$c
x.chi3$e
x.chi3
sum(x.chi3$e)

cut3<-c(min(x)-10,seq(-1.5,1.5,by=.5),max(x)+10)
x.chi3<-chisq.gof(x,cut.points=cut3,dist="norm")
x.chi3
x.chi3$e
x.chi3$c
sum(x.chi3$e)

ks.gof(x,dist="norm")
ks.gof(x,dist="norm",mean=0,sd=1)

x<-rbinom(20,size=5,prob=1/2)
x
table(x)
x<-rbinom(20,size=5,prob=1/2)
table(x)

x<-rbinom(20,size=5,prob=1/2)
table(x)
chisq.gof(x,dist="binom",size=5,prob=1/2)
cut<-quantile(x)
table(cut(x,cut))
chisq.gof(x,cut.points=cut,dist="binom",size=5,prob=1/2)

cut[1]<-cut[1]-1
cut[4]<-cut[4]+1
cut[5]<-cut[5]+1
cut

table(cut(x,cut))

cut<-c(-0.5:5.5,1)
cut
cut<-c(-0.5:5.5)
table(cut(x,cut))
chisq.gof(x,cut.points=cut,dist="binom",size=5,prob=1/2)
chisq.gof(x,cut.points=cut,dist="binom",size=5,prob=1/2)$e
cut<-c(-0.5,1.5:3.5,5.5)
chisq.gof(x,cut.points=cut,dist="binom",size=5,prob=1/2)
chisq.gof(x,cut.points=cut,dist="binom",size=5,prob=1/2)$e


x<-rep(0:7,c(89,143,94,42,20,8,3,1))
 
x
table(x)
cut<-c(0:7)
 
table(cut(x,cut))
cut<-c(-1:7)
 
table(cut(x,cut))
chisq.gof(x,cut.points=cut,n.param.est=1,dist="pois",lambda=mean(x))$e
chisq.gof(x,cut.points=cut,n.param.est=1,dist="pois",lambda=mean(x))$c
cut<-c(-1:4,7)
table(cut(x,cut))
chisq.gof(x,cut.points=cut,n.param.est=1,dist="pois",lambda=mean(x))$e
chisq.gof(x,cut.points=cut,n.param.est=1,dist="pois",lambda=mean(x))
sum(chisq.gof(x,cut.points=cut,n.param.est=1,dist="pois",lambda=mean(x))$e)


%
%  Sign-Test
%
%

set.seed(100)

x<-rnorm(50,3,1)
x

hist(x)
summary(x)

qnorm(0.25,3,1)

x<qnorm(0.25,3,1)

y<-sum(x<qnorm(0.25,3,1))
y

binom.test(y,50,p=0.25)

sign.test<-function(x,p,x0,alternative="two.sided"){
    y<-sum(x<x0)
    n<-length(x)
    return(binom.test(y,n,p,alternative))}

sign.test(x,0.25,2.325)

x<-c(61,69,71,74,79,80,83,84,86,87)
sign.test(x,0.5,72)
2*pbinom(2,10,0.5)
2*pbinom(3,10,0.5)

sign.test(x,0.5,72,"greater")
1-pbinom(2,10,0.5)
1-pbinom(3,10,0.5)


sign.test(x,0.6,72)
pbinom(3,10,0.6)
1-pbinom(1:10,10,0.6)
pbinom(3,10,0.6)+ (1-pbinom(1:10,10,0.6))[8]
pbinom(2,10,0.6)
pbinom(2,10,0.6)+ (1-pbinom(1:10,10,0.6))[9]


%
%
% the p-value is the level of significance for which your
% observed test statistic value t 
% lies on the boundary between acceptance and rejection of the null hypothesis
%
% At any significance level greater than the p-value, you reject the null hypothesis, 
% and at any significance level less than the p-value you accept the null hypothesis
%
%