9.2 Other Distributions
In Section 9.1, we gave a detailed introduction to the four functions for a normal distribution, which is a popular continuous distribution. In particular, we now know that dnorm() produces the pdf of a normal distribution. In the case of discrete distributions, however, we would have probability mass function (pmf) instead of the pdf. Let’s use the binomial distribution as a representative example of discrete distributions with the four functions as below.
| Code | Name |
|---|---|
dbinom(3, size, prob)
|
probability mass function |
pbinom(3, size, prob)
|
cumulative distribution function |
qbinom(3, size, prob)
|
quantile function |
rbinom(3, size, prob)
|
random number generator |
Now, let’s look at a few other commonly used distributions. For simplicity, let’s just use the random number generator for each distribution in the following table.
| Name | Code | para_1 | para_2 |
|---|---|---|---|
| exponential |
rexp(3, rate = 0.5)
|
rate |
|
| uniform |
runif(3, min = 1, max = 2)
|
min | max |
| t |
rt(3, df = 4)
|
df |
|
| F |
rf(3, df1 = 3, df2 = 6)
|
df1 | df2 |
| beta |
rbeta(3, shape1 = 2, shape2 = 3)
|
shape1 | shape2 |
| gamma |
rgamma(3, shape = 2, rate = 3)
|
shape | rate |
| poisson |
rpois(3, lambda = 5)
|
lambda |
|
| binomial |
rbinom(3, size = 3, prob = 0.3)
|
size | prob |
| bernoulli |
rbinom(3, size = 1, prob = 0.5)
|
size | prob |
As we can see from this table, all random number generator functions are formed by the letter r followed by the name of the distribution we would like to generate from. For the other three functions, we just need to change the initial letter r:
- to
dfor pdf (continuous distribution) or pmf (discrete distribution), - to
pfor cdf, - to
qfor quantile function.
Let’s do some statistical exercises with those distributions.