Fitting a density curve to a histogram in R

Question

Is there a function in R that fits a curve to a histogram?

Let's say you had the following histogram

hist(c(rep(65, times=5), rep(25, times=5), rep(35, times=10), rep(45, times=4)))

It looks normal, but it's skewed. I want to fit a normal curve that is skewed to wrap around this histogram.

This question is rather basic, but I can't seem to find the answer for R on the internet.

Stupa

Do you want to find m and s such that the Gaussian distribution N(m,s) fits to your data? – Ticknor

I'm not sure what that means... >_> – Stupa

@mathee: I think he means m = mean, and s = standard deviation. Gaussian distribution is another name for normal distribution. – Unsuitable

Answer 1

If I understand your question correctly, then you probably want a density estimate along with the histogram:

X <- c(rep(65, times=5), rep(25, times=5), rep(35, times=10), rep(45, times=4))
hist(X, prob=TRUE)            # prob=TRUE for probabilities not counts
lines(density(X))             # add a density estimate with defaults
lines(density(X, adjust=2), lty="dotted")   # add another "smoother" density

Edit a long while later:

Here is a slightly more dressed-up version:

X <- c(rep(65, times=5), rep(25, times=5), rep(35, times=10), rep(45, times=4))
hist(X, prob=TRUE, col="grey")# prob=TRUE for probabilities not counts
lines(density(X), col="blue", lwd=2) # add a density estimate with defaults
lines(density(X, adjust=2), lty="dotted", col="darkgreen", lwd=2) 

along with the graph it produces:

Isauraisbel

+1 - can you also do it the other way around, i.e. adjusting the density plot to fit the histogram? – Zito

I suggest giving additional parameter to lines(density(X,na.rm= TRUE) as the vector may contain NA values. – Scandal

I just added a new answer below with a funciton to adjust the density plot to fit the histogram. – Concepcion

Answer 2

Such thing is easy with ggplot2

library(ggplot2)
dataset <- data.frame(X = c(rep(65, times=5), rep(25, times=5), 
                            rep(35, times=10), rep(45, times=4)))
ggplot(dataset, aes(x = X)) + 
  geom_histogram(aes(y = ..density..)) + 
  geom_density()

or to mimic the result from Dirk's solution

ggplot(dataset, aes(x = X)) + 
  geom_histogram(aes(y = ..density..), binwidth = 5) + 
  geom_density()

Conias

Answer 3

Here's the way I do it:

foo <- rnorm(100, mean=1, sd=2)
hist(foo, prob=TRUE)
curve(dnorm(x, mean=mean(foo), sd=sd(foo)), add=TRUE)

A bonus exercise is to do this with ggplot2 package ...

Horme

However, if you want something that is skewed, you can either do the density example from above, transform your data (e.g. foo.log <- log(foo) and try the above), or try fitting a skewed distribution, such as the gamma or lognormal (lognormal is equivalent to taking the log and fitting a normal, btw). – Horme

But that still requires estimating the parameters of your distribution first. – Isauraisbel

This gets a bit far afield from simply discussing R, as we are getting more into theoretical statistics, but you might try this link for the Gamma: en.wikipedia.org/wiki/Gamma_distribution#Parameter_estimation For lognormal, just take the log (assuming all data is positive) and work with log-transformed data. For anything fancier, I think you would have to work with a statistics textbook. – Horme

I think you misunderstand how both the original poster as well as all other answers are quite content to use non-parametric estimates -- like an old-school histogram or a somewhat more modern data-driven densisty estimate. Parametric estimates are great if you have good reason to suspect a distribution. But that was not the case here. – Isauraisbel

Answer 4

Dirk has explained how to plot the density function over the histogram. But sometimes you might want to go with the stronger assumption of a skewed normal distribution and plot that instead of density. You can estimate the parameters of the distribution and plot it using the sn package:

> sn.mle(y=c(rep(65, times=5), rep(25, times=5), rep(35, times=10), rep(45, times=4)))
$call
sn.mle(y = c(rep(65, times = 5), rep(25, times = 5), rep(35, 
    times = 10), rep(45, times = 4)))

$cp
    mean     s.d. skewness 
41.46228 12.47892  0.99527 

This probably works better on data that is more skew-normal:

Sarthe

Answer 5

I had the same problem but Dirk's solution didn't seem to work. I was getting this warning messege every time

"prob" is not a graphical parameter

I read through ?hist and found about freq: a logical vector set TRUE by default.

the code that worked for me is

hist(x,freq=FALSE)
lines(density(x),na.rm=TRUE)

Serrulation

Answer 6

It's the kernel density estimation, and please hit this link to check a great illustration for the concept and its parameters.

The shape of the curve depends mostly on two elements: 1) the kernel(usually Epanechnikov or Gaussian) that estimates a point in the y coordinate for every value in the x coordinate by inputting and weighing all data; and it is symmetric and usually a positive function that integrates into one; 2) the bandwidth, the larger the smoother the curve, and the smaller the more wiggled the curve.

For different requirements, different packages should be applied, and you can refer to this document: Density estimation in R. And for multivariate variables, you can turn to the multivariate kernel density estimation.

Rheims

Answer 7

Some comments requested scaling the density estimate line to the peak of the histogram so that the y axis would remain as counts rather than density. To achieve this I wrote a small function to automatically pull the max bin height and scale the y dimension of the density function accordingly.

hist_dens <- function(x, breaks = "Scott", main = "title", xlab = "x", ylab = "count") {
  
  dens <- density(x, na.rm = T)
  
  raw_hist <- hist(x, breaks = breaks, plot = F)
  
  scale <- max(raw_hist$counts)/max(raw_hist$density)
  
  hist(x, breaks = breaks, prob = F, main = main, xlab = xlab, ylab = ylab)
  
  lines(list(x = dens$x, y = scale * dens$y), col = "red", lwd = 2)
  
}

hist_dens(rweibull(1000, 2))

^{Created on 2021-12-19 by the reprex package (v2.0.1)}

Concepcion