Tarea_4.R

library(spatstat)

## Loading required package: spatstat.data

## Loading required package: nlme

## Loading required package: rpart

## 
## spatstat 1.56-1       (nickname: 'Invisible Friend') 
## For an introduction to spatstat, type 'beginner'

###################Distribucion Normal
######correlación de 1 
Xx1<- rnorm(10000,5,1.5)
hist(Xx1)

Yy1<- Xx1
hist(Yy1)

cor(Xx1,Yy1)

## [1] 1

Ppp1 <- ppp(Xx1,Yy1,c(min(Xx1),max(Xx1)),c(min(Yy1),max(Yy1)))
Den1 <- density(Ppp1)
plot(Xx1,Yy1)

contour(Den1)

persp(Den1)

#######Correlacion de -1
r<- -1
Xx2<- rnorm(10000,5,1.5)
hist(Xx2)

y2 <- rnorm(10000,5,1.5)
Yy2 <- r*Xx2 + sqrt(1-r^2)*y2
hist(Yy2)

cor(Xx2,Yy2)

## [1] -1

Ppp2 <- ppp(Xx2,Yy2,c(min(Xx2),max(Xx2)),c(min(Yy2),max(Yy2)))
Den2 <- density(Ppp2)
plot(Xx2,Yy2)

contour(Den2)

persp(Den2)

#######Correlacion de 0.5
r<- 0.5
Xx3<- rnorm(10000,5,1.5)
hist(Xx3)

y3 <- rnorm(10000,5,1.5)
Yy3 <- r*Xx3 + sqrt(1-r^2)*y3
hist(Yy3)

cor(Xx3,Yy3)

## [1] 0.4898985

Ppp3 <- ppp(Xx3,Yy3,c(min(Xx3),max(Xx3)),c(min(Yy3),max(Yy3)))
Den3 <- density(Ppp3)
plot(Xx3,Yy3)

contour(Den3)

persp(Den3)

#######Correlacion de -0.5
r<- -0.5
Xx4<- rnorm(10000,5,1.5)
hist(Xx4)

y4 <- rnorm(10000,5,1.5)
Yy4 <- r*Xx4 + sqrt(1-r^2)*y4
hist(Yy4)

cor(Xx4,Yy4)

## [1] -0.5099316

Ppp4 <- ppp(Xx4,Yy4,c(min(Xx4),max(Xx4)),c(min(Yy4),max(Yy4)))
Den4 <- density(Ppp4)
plot(Xx4,Yy4)

contour(Den4)

persp(Den4)

#######Correlacion de 0
r<- 0
Xx5<- rnorm(10000,5,1.5)
hist(Xx5)

y5 <- rnorm(10000,5,1.5)
Yy5 <- r*Xx5 + sqrt(1-r^2)*y5
hist(Yy5)

cor(Xx5,Yy5)

## [1] 0.002268939

Ppp5 <- ppp(Xx5,Yy5,c(min(Xx5),max(Xx5)),c(min(Yy5),max(Yy5)))
Den5 <- density(Ppp5)
plot(Xx5,Yy5)

contour(Den5)

persp(Den5)

###################Distribucion Exponencial
######correlación de 1
r<- 1
Xx6<- rexp(10000,1.5)
hist(Xx6)

y6 <- rexp(10000,1.5)
Yy6 <- r*Xx6 + sqrt(1-r^2)*y6
hist(Yy6)

cor(Xx6,Yy6)

## [1] 1

Ppp6 <- ppp(Xx6,Yy6,c(min(Xx6),max(Xx6)),c(min(Yy6),max(Yy6)))
Den6 <- density(Ppp6)
plot(Xx6,Yy6)

contour(Den6)

persp(Den6)

######correlación de -1
r<- -1
Xx7<- rexp(10000,1.5)
hist(Xx7)

y7 <- rexp(10000,1.5)
Yy7 <- r*Xx7 + sqrt(1-r^2)*y7
hist(Yy7)

cor(Xx7,Yy7)

## [1] -1

Ppp7 <- ppp(Xx7,Yy7,c(min(Xx7),max(Xx7)),c(min(Yy7),max(Yy7)))
Den7 <- density(Ppp7)
plot(Xx7,Yy7)

contour(Den7)

persp(Den7)

######correlación de 0.5
r<- 0.5
Xx8<- rexp(10000,1.5)
hist(Xx8)

y8 <- rexp(10000,1.5)
Yy8 <- r*Xx8 + sqrt(1-r^2)*y8
hist(Yy8)

cor(Xx8,Yy8)

## [1] 0.5080111

Ppp8 <- ppp(Xx8,Yy8,c(min(Xx8),max(Xx8)),c(min(Yy8),max(Yy8)))
Den8 <- density(Ppp8)
plot(Xx8,Yy8)

contour(Den8)

persp(Den8)

######correlación de -0.5
r<- -0.5
Xx9<- rexp(10000,1.5)
hist(Xx9)

y9 <- rexp(10000,1.5)
Yy9 <- r*Xx9 + sqrt(1-r^2)*y9
hist(Yy9)

cor(Xx9,Yy9)

## [1] -0.5019202

Ppp9 <- ppp(Xx9,Yy9,c(min(Xx9),max(Xx9)),c(min(Yy9),max(Yy9)))
Den9 <- density(Ppp9)
plot(Xx9,Yy9)

contour(Den9)

persp(Den9)

######correlación de 0
r<- 0
Xx10<- rexp(10000,1.5)
hist(Xx10)

y10 <- rexp(10000,1.5)
Yy10 <- r*Xx10 + sqrt(1-r^2)*y10
hist(Yy10)

cor(Xx10,Yy10)

## [1] -0.005518881

Ppp10 <- ppp(Xx10,Yy10,c(min(Xx10),max(Xx10)),c(min(Yy10),max(Yy10)))
Den10 <- density(Ppp10)
plot(Xx10,Yy10)

contour(Den10)

persp(Den10)

###################Distribucion Uniforme
######correlación de 1
r<- 1
Xx11<- runif(10000,0,50)
hist(Xx11)

y11 <- runif(10000,0,50)
Yy11 <- r*Xx11 + sqrt(1-r^2)*y11
hist(Yy11)

cor(Xx11,Yy11)

## [1] 1

Ppp11 <- ppp(Xx11,Yy11,c(min(Xx11),max(Xx11)),c(min(Yy11),max(Yy11)))
Den11 <- density(Ppp11)
plot(Xx11,Yy11)

contour(Den11)

persp(Den11)

######correlación de -1
r<- -1
Xx12<- runif(10000,0,50)
hist(Xx12)

y12 <- runif(10000,0,50)
Yy12 <- r*Xx12 + sqrt(1-r^2)*y12
hist(Yy12)

cor(Xx12,Yy12)

## [1] -1

Ppp12 <- ppp(Xx12,Yy12,c(min(Xx12),max(Xx12)),c(min(Yy12),max(Yy12)))
Den12 <- density(Ppp12)
plot(Xx12,Yy12)

contour(Den12)

persp(Den12)

######correlación de 0.5
r<- 0.5
Xx13<- runif(10000,0,50)
hist(Xx13)

y13 <- runif(10000,0,50)
Yy13 <- r*Xx13 + sqrt(1-r^2)*y13
hist(Yy13)

cor(Xx13,Yy13)

## [1] 0.5136526

Ppp13 <- ppp(Xx13,Yy13,c(min(Xx13),max(Xx13)),c(min(Yy13),max(Yy13)))
Den13 <- density(Ppp13)
plot(Xx13,Yy13)

contour(Den13)

persp(Den13)

######correlación de -0.5
r<- -0.5
Xx14<- runif(10000,0,50)
hist(Xx14)

y14 <- runif(10000,0,50)
Yy14 <- r*Xx14 + sqrt(1-r^2)*y14
hist(Yy14)

cor(Xx14,Yy14)

## [1] -0.4891956

Ppp14 <- ppp(Xx14,Yy14,c(min(Xx14),max(Xx14)),c(min(Yy14),max(Yy14)))
Den14 <- density(Ppp14)
plot(Xx14,Yy14)

contour(Den14)

persp(Den14)

######correlación de 0
r<- 0
Xx15<- runif(10000,0,50)
hist(Xx15)

y15 <- runif(10000,0,50)
Yy15 <- r*Xx15 + sqrt(1-r^2)*y15
hist(Yy15)

cor(Xx15,Yy15)

## [1] 0.002470766

Ppp15 <- ppp(Xx15,Yy15,c(min(Xx15),max(Xx15)),c(min(Yy15),max(Yy15)))
Den15 <- density(Ppp15)
plot(Xx15,Yy15)

contour(Den15)

persp(Den15)