How to draw a QQ plot in R?

Question

The task:

To draw a quantile-quantile (Q-Q) plot to check whether the gamma distribution is a good model for my data without relying on qqplot. To judge the goodness of fit in this Q-Q plot, draw Q-Q plots for three sets of 150 observations generated from your fitted Gamma distribution.

So I have 150 observations which I have modelled as a Gamma distribution and found estimates for k and lambda:

pp = c(1:150)/151
qq= qgamma(pp,k,rate=lambda)
layout(matrix(c(1,1,2,3), 2, 2, byrow = TRUE))
plot(qq,sort(x),main="Q-Q plot with gamma distribution",xlab='Quantiles of gamma distribution',ylab="Ordered data")

However when I plot qq individually 3 times it comes up with exactly the same graph?

Answer 1

I assume you have a vector x with your observed Gamma-distributed observations; I further assume you know the shape and rate parameters of the underlying Gamma distribution, and that you want to compare your observed quantiles to theoretical quantiles from a Gamma distribution with the same shape and rate parameters.

Here is an example, where I generate data x from a Gamma distribution with shape = 2 and rate = 1 parameter.

# Set seed for reproducibility
set.seed(2017);

# Generate some Gamma distributed data
x <- rgamma(100, shape = 2, rate = 1);

# Sort x values
x <- sort(x);

# Theoretical distribution
x0 <- qgamma(ppoints(length(x)), shape = 2, rate = 1);

plot(x = x0, y = x, xlab = "Theoretical quantiles", ylab = "Observed quantiles");
abline(a = 0, b = 1, col = "red");