Simulation is important topic for statistical applications and scientific purposes in general.
Generating Random Numbers
The first step in simulation is to generate random values based on your variables distribution. R has a large number of functions that generate the standard random variables.
for Normal random variable generation
rnorm() simulate a simple random normal variable with a given mean and standard deviation and generate as many random values as requested.
When generating any random variable setting the random number seed with set.seed ensures reproducibility. In the following example, notice that the first and the third sets are identical (both called set.seed with 1 before generating the numbers), and the second is different (because we didn’t set the seed)
for Poisson random variable generation
rpois() simulate a Poisson random variable with a given rate (lambda) and generate as many random values as requested.
Radom sampling
The sample function draws randomly from a specified set of (scalar) objects allowing you to sample from arbitrary distributions (sample space).
if you didn’t specified the number of values you want, sample will give you random permutation of the sequence.
as you noticed, by default sample will not repeat values, set parameter replace= TRUE to make it repeat .
Probability distribution functions
Probability distributions usually have four functions associated with them. The functions are prefixed with:
- r for random number generation
- d for density
- p for cumulative distribution
- q for quantile function
some useful distributions are:
| Nickname | Distribution | For more information |
| norm | normal distribution | ?Normal |
| pois | poisson distribution | ?Possion |
| binom | binomial distribution | ?Binomial |
| geom | geometric distribution | ?Geometric |
| t | students t distribution | ?TDist |
| f | F distribution | ?FDist |
| chisq | Chi-Squared distribution | ?Chisquare |
function names are : prefix + distribution nickname. rnorm, rpois, rbinom,….. –> for random number generation, and so on.
In this note we introduced the basic functions for random number generation based on variable distribution type, arbitrary random sampling, and the associated probability distributions functions. Later will present each of them in detail.
Stay tuned for more R notes.
