library(ggplot2)
set.seed(1)
dataset <- data.frame(X = rnorm(1000))
dfun <- function(x, a, b) 1/(sqrt(2*pi)*b)*exp(-0.5*((x-a)^2/(2*b^2)))
ggplot(dataset, aes(x = X)) +
geom_histogram(aes(y = ..density..), binwidth = 0.5)+
stat_function(fun = dfun,
args = list(a = , b = ))
How can I calculate suitable values of a and b in case like this?
You can compute values for the arguments a and b with nls. Something like the following.
dens <- density(dataset$X, n = nrow(dataset))
df_dens <- data.frame(x = dens$x, y = dens$y)
a0 <- mean(dataset$X)
b0 <- sd(dataset$X)
fit <- nls(y ~ dfun(x, a, b), data = df_dens, start = list(a = a0, b = b0))
coef(fit)
# a b
#-0.007006625 0.97518478
Now plot the histogram and the function with these values for a and b.
ggplot(dataset, aes(x = X)) +
geom_histogram(aes(y = ..density..), binwidth = 0.5)+
stat_function(fun = dfun,
args = list(a = coef(fit)[1], b = coef(fit)[2]))
