# If you donft install sgt package in your R software, firstly please run this R code .
install.packages("sgt", dependencies = TRUE)

#Condition 1-------------------------------------------------------------------
datasetA1 <- c(0.0149*1.05, 0.0149*1.025, 0.0149, 0.0149*0.975, 0.0149*0.95)
datasetA1
logA1 <- log(datasetA1)
logA1
meanA1 <- mean(logA1)
meanA1
varA1 <- var(logA1)
varA1
library(sgt)#package optimx and numDeriv are need to use sgt package 
log(0.0334)
x <- seq(-8, 0, 0.01)
plot(x, dsgt(x, mu=meanA1, sigma = sqrt((1+1/5)*varA1^2), lambda = 0, p=2, q=5/2), type="n")
curve(dsgt(x, mu=meanA1, sigma = sqrt((1+1/5)*varA1^2), lambda = 0, p=2, q=5/2), type="l", add="T")
par(new=T)
px <- c(0, 0, 0, 0, 0)
points(logA1, px)
lower_limit <- log(0.0334)
abline(v=lower_limit)
psgt(lower_limit, mu=meanA1, sigma = sqrt((1+1/5)*varA1^2), lambda = 0, p=2, q=5/2)

#Condition 2-------------------------------------------------------------------
datasetA2 <- c(0.0149*1.5, 0.0149*1.25, 0.0149, 0.0149*0.75, 0.0149*0.5)
datasetA2
logA2 <- log(datasetA2)
logA2
meanA2 <- mean(logA2)
meanA2
varA2 <- var(logA2)
varA2
library(sgt)#package optimx and numDeriv are need to use sgt package 
log(0.0334)
x <- seq(-8, 0, 0.01)
plot(x, dsgt(x, mu=meanA2, sigma = sqrt((1+1/5)*varA2^2), lambda = 0, p=2, q=5/2), type="n")
curve(dsgt(x, mu=meanA2, sigma = sqrt((1+1/5)*varA2^2), lambda = 0, p=2, q=5/2), type="l", add="T")
par(new=T)
px <- c(0, 0, 0, 0, 0)
points(logA2, px)
lower_limit <- log(0.0334)
abline(v=lower_limit)
psgt(lower_limit, mu=meanA2, sigma = sqrt((1+1/5)*varA2^2), lambda = 0, p=2, q=5/2)

#Condition 3-------------------------------------------------------------------
datasetA3 <- c(0.0149*1.64, 0.0149*1.32, 0.0149, 0.0149*0.68, 0.0149*0.36)
datasetA3
logA3 <- log(datasetA3)
logA3
meanA3 <- mean(logA3)
meanA3
varA3 <- var(logA3)
varA3
library(sgt)#package optimx and numDeriv are need to use sgt package 
log(0.0334)
x <- seq(-8, 0, 0.01)
plot(x, dsgt(x, mu=meanA3, sigma = sqrt((1+1/5)*varA3^2), lambda = 0, p=2, q=5/2), type="n")
curve(dsgt(x, mu=meanA3, sigma = sqrt((1+1/5)*varA3^2), lambda = 0, p=2, q=5/2), type="l", add="T")
par(new=T)
px <- c(0, 0, 0, 0, 0)
points(logA3, px)
lower_limit <- log(0.0334)
abline(v=lower_limit)
psgt(lower_limit, mu=meanA3, sigma = sqrt((1+1/5)*varA3^2), lambda = 0, p=2, q=5/2)

#Condition 4-------------------------------------------------------------------
datasetA4 <- c(0.0149*1.82, 0.0149*1.41, 0.0149, 0.0149*0.59, 0.0149*0.18)
datasetA4
logA4 <- log(datasetA4)
logA4
meanA4 <- mean(logA4)
meanA4
varA4 <- var(logA4)
varA4
library(sgt)#package optimx and numDeriv are need to use sgt package 
log(0.0334)
x <- seq(-8, 0, 0.01)
plot(x, dsgt(x, mu=meanA4, sigma = sqrt((1+1/5)*varA4^2), lambda = 0, p=2, q=5/2), type="n")
curve(dsgt(x, mu=meanA4, sigma = sqrt((1+1/5)*varA4^2), lambda = 0, p=2, q=5/2), type="l", add="T")
par(new=T)
px <- c(0, 0, 0, 0, 0)
points(logA4, px)
lower_limit <- log(0.0334)
abline(v=lower_limit)
psgt(lower_limit, mu=meanA4, sigma = sqrt((1+1/5)*varA4^2), lambda = 0, p=2, q=5/2)