Example of fitting marginal distributions to histogram in R - r

Question

Could someone show me how to fit a polynomial marginal distribution to my data? I have done a binomial and beta binomial, but I would like to see how to fit a polynomial. I would also be interested in trying a gamma if that is something you know how to do.
This is what I have done so far.
nodes <- read.table("https://web.stanford.edu/~hastie/CASI_files/DATA/nodes.txt",
header = T)
nodes %>%
ggplot(aes(x=x/n))+
geom_histogram(bins = 30)+
theme_bw()+
labs(x = "nodes",
n = "p=x/n")
# log-likelihood function
ll <- function(alpha, beta) {
x <- nodes$x
total <- nodes$n
-sum(VGAM::dbetabinom.ab(x, total, alpha, beta, log = TRUE))
}
# maximum likelihood estimation
m <- mle(ll, start = list(alpha = 1, beta = 10), method = "L-BFGS-B",
lower = c(0.0001, .1))
ab <- coef(m)
alpha0 <- ab[1]
beta0 <- ab[2]
nodes %>%
ggplot() +
geom_histogram(aes(x/n, y = ..density..), bins= 30) +
stat_function(fun = function(x) dbeta(x, alpha0, beta0), color = "red",
size = 1) +
xlab("p=x/n")
Here is another fit
ll <- function(a){
x <- nodes$x
total <- nodes$n
-sum(stats::dbinom(x, total, a, log = TRUE))
}
#stats::dbinom()
m <- mle(ll, start = list(a=.5), method = "L-BFGS-B",
lower = c(0.0001, .1))
a = coef(m)
nodes %>%
ggplot() +
geom_histogram(aes(x/n, y = ..density..), bins=40) +
stat_function(fun = function(x) dbeta(x, a, 1), color = "red",
size = 1) +
xlab("proportion x/n")

Answer 1

For fitting a gamma distribution:
data(iris)
library(MASS) ##for the fitdistr function
fit.params <- fitdistr(iris$Sepal.Length, "gamma", lower = c(0, 0))
ggplot(data = iris) +
geom_histogram(data = as.data.frame(x), aes(x=iris$Sepal.Length, y=..density..)) +
geom_line(aes(x=iris$Sepal.Length,
y=dgamma(iris$Sepal.Length,fit.params$estimate["shape"],
fit.params$estimate["rate"])), color="red", size = 1) +
theme_classic()
You might also like to take a look at the distribution of the quantiles using the qqp function in the car package. Here are a few examples:
library(car)
qqp(iris$Sepal.Length, "norm") ##normal distribution
qqp(iris$Sepal.Length, "lnorm") ##log-normal distribution
gamma <- fitdistr(iris$Sepal.Length, "gamma")
qqp(iris$Sepal.Length, "gamma", shape = gamma$estimate[[1]],
rate = gamma$estimate[[2]]) ##gamma distribution
nbinom <- fitdistr(iris$Sepal.Length, "Negative Binomial")
qqp(iris$Sepal.Length, "nbinom", size = nbinom$estimate[[1]],
mu = nbinom$estimate[[2]]) ##negative binomial distribution
You can use the fitdistr function for ggplots or qqPlots. It supports lots of different distributions. Take a look at ?fitdistr