#Create and view distributions

mynormal <- rnorm(n =10000, mean = 85, sd = 40)
mylognormal <- rlnorm(n=10000, meanlog = 1, sdlog = 0.1)
mybeta <- rbeta(n=10000, shape1=1, shape2=99)
mybinary <-rbinom(n=10000,size=1, prob=0.95)
mybinomial <- rbinom(n=10000, size=2000, prob=0.95)
myexponential <- rexp(n=10000, rate=4.2)
mygamma <- rgamma(n=10000, shape=2, rate=2) #rgamma(n, shape, rate = 1, scale = 1/rate)
mygeometric <- rgeom(n=10000, prob=0.10)
mynegbinomial <- rnbinom(n=10000, size=1000, prob=0.97)
mypoisson <- rpois(n=10000, lambda=10)

hist(mynormal)
hist(mylognormal)
hist(mybeta)
hist(mybinary)
hist(mybinomial)
hist(myexponential)
hist(mygamma)
hist(mygeometric)
hist(mynegbinomial)
hist(mypoisson)

  #can change around the parameters
#----------------------------------------------------------------------------------------------------------------------------;

#Examples of distributions in action
library(Stat2Data)
library(ggplot2)

#Normal
data("AppleStock")
head(AppleStock)
hist(AppleStock$Change) #normal

glm1 <-glm(Change~Volume, data=AppleStock, family=gaussian())
summary(glm1)

plot1 <-ggplot(data=AppleStock, aes(x=Volume, y=Change))+
  geom_hline(aes(yintercept=0), size=2)+
  geom_point(col="blue")+
  geom_smooth(method=lm, col="red")
plot1
#----------------------------------------------------------


#Binary
data("WalkTheDogs")
head(WalkTheDogs)
hist(WalkTheDogs$Walk)
glm2 <-glm(Walk~Kcal, data=WalkTheDogs, family=binomial())
summary(glm2)

plot2 <-ggplot(data=WalkTheDogs, aes(x=Kcal, y=Walk))+
  geom_point(col="blue")+
  stat_smooth(method="glm", method.args=list(family=binomial), color="red", size=1)
plot2
#----------------------------------------------------------


#Binomial
data("FGByDistance")
head(FGByDistance)
hist(FGByDistance$Makes)
glm3 <- glm(cbind(Makes,N-Makes)~Dist, data=FGByDistance, family=binomial())
summary(glm3)

plot3 <-ggplot(data=FGByDistance, aes(x=Dist, y=PropMakes))+
  geom_point(col="blue")+
  stat_smooth(method="glm", method.args=list(family=binomial), color="red", size=1)
plot3
#----------------------------------------------------------


#Gamma
data("HorsePrices")
hist(HorsePrices$Price)
glm4 <-glm(Price~Height, data=HorsePrices, family=Gamma())
summary(glm4)

plot4 <-ggplot(data=HorsePrices, aes(x=Height, y=Price))+
  geom_point(col="blue")+
  stat_smooth(method="glm", method.args=list(family=Gamma), color="red", size=1)
plot4
#----------------------------------------------------------


#Poisson
data("GlowWorms") 
hist(GlowWorms$Eggs)
glm5 <-glm(Eggs~Lantern, data=GlowWorms, family=poisson())
summary(glm5)

plot5 <-ggplot(data=GlowWorms, aes(x=Lantern, y=Eggs))+
  geom_point(col="blue")+
  stat_smooth(method="glm", method.args=list(family=poisson), color="red", size=1)
plot5
#----------------------------------------------------------


#References:
  #Distributions in the stats package
  #https://stackoverflow.com/questions/14048401/simulate-data-from-lognormal-in-r
  
  #https://dnett.github.io/S510/27GLMbinomialAnnotated.PDF

  #https://tysonbarrett.com/Rstats/chapter-5-generalized-linear-models.html