library(brms)

######shape=1 and scale = 4
w<-rweibull(n=300, shape = 1, scale = 4)
w<-data.frame(w)
m<-brm(w~1,data=w,family=weibull())
m
s1 <- posterior_samples(m)

#recover scale and shape parameters
#scale
mean(exp(s1$b_Intercept))
#shape
mean(s1$shape)

###predict mean
summary(w)
f<-fitted(m)
summary(f)

#this way?
mean(exp(s1$b_Intercept * (gamma(1 + 1/exp(s1$shape)))))

#or this?
mean(exp(s1$b_Intercept * (gamma(1 + 1/(s1$shape)))))

#or this?
mean(exp(s1$b_Intercept) * (gamma(1 + 1/(s1$shape))))





######shape=10 and scale = 15
w<-rweibull(n=300, shape = 10, scale = 15)
w<-data.frame(w)
m<-brm(w~1,data=w,family=weibull())
m
s1 <- posterior_samples(m)

#recover scale and shape parameters
#scale
mean(exp(s1$b_Intercept))
#shape
mean(s1$shape)

###predict mean
summary(w)
f<-fitted(m)
summary(f)

#this way?
mean(exp(s1$b_Intercept * (gamma(1 + 1/exp(s1$shape)))))

#or this?
mean(exp(s1$b_Intercept * (gamma(1 + 1/(s1$shape)))))

#or this?
mean(exp(s1$b_Intercept) * (gamma(1 + 1/(s1$shape))))