Plotting the normal and binomial distribution in same plot

user_1048781 0
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As the title indicates I am trying to plot the normal distribution and the binomial distribution in the same plot using R. My attempt can be seen below, is there any reason why my normal distribution looks so off? I have double checked the mean and standard deviation and everything looks fine.

enter image description here

n <- 151
p <- 0.2409

dev <- 4
mu <- n*p
sigma <- sqrt(n*p*(1 - p))

xmin <- round(max(mu - dev*sigma,0));
xmax <- round(min(mu + dev*sigma,n))
x <- seq(xmin, xmax)
y <- dbinom(x,n,p)

barplot(y, 
     col = 'lightblue',
     names.arg = x,
     main = 'Binomial distribution, n=151, p=.803')

range <- seq(mu - dev*sigma, mu + dev*sigma, 0.01)
height <- dnorm(range, mean = mu, sd = sigma) 
lines(range, height, col = 'red', lwd = 3)
normal-distribution distribution plot r
3 Answers

barplot is just the wrong function for your case. Or if you really want to use it, you'd have to rejigger the x-axes between barplot and lines

The default for barplot is to put each height value at

head(c(barplot(y, plot = FALSE)))
# [1] 0.7 1.9 3.1 4.3 5.5 6.7

This can be changed by your choices of space and width or a combination of both

head(c(barplot(y, plot = FALSE, space = 0)))
# [1] 0.5 1.5 2.5 3.5 4.5 5.5

head(c(barplot(y, plot = FALSE, space = 0, width = 3)))
# [1]  1.5  4.5  7.5 10.5 13.5 16.5

You can just use plot to avoid dealing with those things

n <- 151
p <- 0.2409

dev <- 4
mu <- n*p
sigma <- sqrt(n*p*(1 - p))

xmin <- round(max(mu - dev*sigma,0));
xmax <- round(min(mu + dev*sigma,n))
x <- seq(xmin, xmax)
y <- dbinom(x,n,p)

plot(x, y, type = 'h', lwd = 10, lend = 3, col = 'lightblue',
     ann = FALSE, las = 1, bty = 'l', yaxs = 'i', ylim = c(0, 0.08))
title(main = sprintf('Binomial distribution, n=%s, p=%.3f', n, p))
lines(x, dnorm(x, mean = mu, sd = sigma), col = 'red', lwd = 7)

xx <- seq(min(x), max(x), length.out = 1000)
lines(xx, dnorm(xx, mean = mu, sd = sigma), col = 'white')

enter image description here

The "bars" in this figure depend on your choice of lwd and your device dimensions, but if you need finer control over that, you can use rect which takes a little more work.

w <- 0.75
plot(x, y, type = 'n', ann = FALSE, las = 1, bty = 'l', yaxs = 'i', ylim = c(0, 0.08))
rect(x - w / 2, 0, x + w / 2, y, col = 'lightblue')
lines(xx, dnorm(xx, mean = mu, sd = sigma), col = 'red', lwd = 3)
title(main = sprintf('Binomial distribution, n=%s, p=%.3f', n, p))

enter image description here

user_29949490

You can use the ggplot2 package

library(ggplot2)

n <- 151
p <- 0.2409
mean <- n*p
sd <-   sqrt(n*p*(1-p))
binwidth <-   0.005


xmin <- round(max(mu - dev*sigma,0));
xmax <- round(min(mu + dev*sigma,n))
x <- seq(xmin, xmax)
y <- dbinom(x,n,p)

df <- cbind.data.frame(x, y)

ggplot(df, aes(x = x, y = y)) +
  geom_bar(stat="identity", fill = 'dodgerblue3')+
  labs(title = "Binomial distribution, n=151, p=.803",
       x = "",
       y = "") +
  theme_minimal()+
  # Create normal curve, akousting for number of observations and binwidth
  stat_function( 
    fun = function(x, mean, sd, n, bw){ 
      dnorm(x = x, mean = mean, sd = sd)
    }, col = "red", size=I(1.4),  
    args = c(mean = mean, sd = sd, n = n, bw = binwidth))

enter image description here

user_97789460

You could do it using the ggplot2 package (I was surprised by the normal distribution but replacing geom_line by geom_point convinced me that is has this form (is the variance too high ?)) :

n <- 151
p <- 0.2409

dev <- 4
mu <- n*p
sigma <- sqrt(n*p*(1 - p))

xmin <- round(max(mu - dev*sigma,0));
xmax <- round(min(mu + dev*sigma,n))

x <- seq(xmin, xmax)
y <- dbinom(x,n,p)

z <- dnorm(x = qnorm(p = seq(0,1, length.out = length(x)), mean = mu, sd = sigma), mean = mu, sd = sigma)

library(magrittr)
library(ggplot2)
data.frame(x, y, z) %>% 
    ggplot(aes(x = x)) +
    geom_col(aes(y = y)) +
    geom_line(aes(x = x, y = z, colour = "red"),
          show.legend = FALSE)

user_109834700
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