how to check Goodness of fit for Gamma Distribution, Weibull Distribution, Exponential Distribution with Anderson Darling Test

[daisha]

how to check Goodness of fit for Gamma Distribution, Weibull Distribution, Exponential Distribution with Anderson Darling Test?

[fcas80]

Anderson-Darling Test is a goodness-of-fit test that determines how well your data fits a given distribution.

df <- data.frame(body_fat=
c(25.3, 29.3, 37.7, 32.8, 24.6, 26.5, 21.2, 28.4, 24.0, 28.7, 37.4, 30.7, 36.7, 28.2, 26.4,
37.1, 31.1, 43.1, 34.1, 26.7, 30.9, 30.0, 22.1, 24.4, 22.5, 24.9, 18.2, 25.9, 28.3, 18.7,
22.4, 23.6, 26.8, 17.8, 27.4, 16.8, 26.1, 20.8, 22.7, 20.2, 20.3, 31.9, 22.9, 25.3, 17.3,
41.0, 25.8, 36.6, 27.8, 39.4, 36.4, 46.8, 40.5, 43.0, 39.5, 39.4, 24.8, 35.0, 25.3, 42.5,
27.8, 35.8, 39.2, 38.3, 34.1, 39.9, 32.5, 29.9, 32.0, 23.0, 28.5, 26.4, 33.9, 29.4, 29.4,
21.0, 22.4, 25.3, 20.2, 22.5, 23.4, 29.5, 21.9, 19.2, 28.6, 23.4, 23.2, 18.1, 31.4, 22.9, 25.6))
hist(df$body_fat,
breaks=12,
xlim=c(10,50),
col="blue",
border="black",
ylim=c(0,16),
xlab="% Fat",
ylab="Counts",
main="Histogram of % Body Fat")
library(cmstatr)
library(gofgamma)
anderson_darling_normal(x=df$body_fat, alpha = 0.05)
anderson_darling_lognormal(x=df$body_fat, alpha = 0.05)
anderson_darling_weibull(x=df$body_fat, alpha = 0.05)
gofgamma::test.AD(data=df$body_fat, boot = 500, alpha = 0.05) # Gamma