Functions
Built-in function with R
Just like most packages, R has many built-in functions. Below is the list of some, x being a vector or a matrix.
Arithmetic operations
| Operation | Description |
| + | Addition |
| - | Substraction |
| * | Multiplication |
| / | Division |
| ** or ^ | Exponentiation |
Numerical Functions (The list is by ne means exhaustive!)
| Function | Description |
| abs(x) | absolute value |
| sqrt(x) | square root |
| ceiling(x) | ceiling(3.475) is 4 |
| floor(x) | floor(3.475) is 3 |
| trunc(x) | trunc(5.99) is 5 |
| round(x, digits=n) | round(3.475, digits=2) is 3.48 |
| signif(x, digits=n) | signif(3.475, digits=2) is 3.5 |
| cos(x), sin(x), tan(x) acos(x), cosh(x), acosh(x), etc.. |
cosine(x), sine(x), arcosine(x) hyperbolic cosine(x), hyperbolic arcosine(x),etc.. |
| log(x) | natural logarithm ln(x) |
| log10(x) | logarithm base 10 of x |
| exp(x) | exponential of x |
Statistical Functions (The list is by ne means exhaustive!)
| Function | Description |
| mean(x, trim=r , na.rm=FALSE) | r % trimmed mean of object x |
| sd(x) | standard deviation of object x |
| var(x) | variance of object x |
| mad(x) | median absolute deviation of object x |
| median(x) | median of object x |
| range(x) | range of object x |
| sum(x) | sum of the values of objet x |
| min(x) | minimum value of object x |
| max(x) | maximum values of object x |
Statistical Distribution Functions
Given a random variable X, taking values x, one is usually interested in four quantities:
- f(x), where f() is the p.d.f (probability density function) or the p.m.f of X,
- F(x) ,where F() is the c.d.f (cumulative probability distribution) of X,
- quantile(p) , where quantile() is the p-th quantile of the distribution of X,
- random(n), where random() is a random generator of n points from the distribution of X.
R already has some distribution encoded and the syntax is as follows. Suppose the distribution of X is mydistribution.
then
| Function | Description |
| dmydistribition(x) | density function f(x) |
| pmydistribution(x) | cumulative distribution F(x) |
| qmydistribution(p) | pth-quantile rfom the distribution of X |
| rmydistribution(n) | n random numbers from the distribution of X |
Some distribution names include
| mydistribution | Description |
| unif | Uniform distribution |
| norm | Normal distribution |
| exp | Exponential distribution |
| t | Student-t distribution |
| gamma | Gamma distribution |
| chisq | Chi-squared distribution |
| lnorm | Log-normal distribution |
| weibill | Weibull distribution |
| cauchy | Cauchy distribution |
| binom | Binomial distribution |
| pois | Poisson distribution |
| geom | Geometric distribution |
| hyper | Hypergeometric distribution |
Example of use:
Suppose X is normally distributed with mean 2 and standard deviation 1, and we want: (a) P(X<1.65) (b) Find x such that P(X>x)=0.05. (c) Generate 5 random point from the distribution of X.
We would do sequentially the following:
>pnorm(1.65,2,1,lower.tail=TRUE) # Question (a)
[1] 0.3631693
>qnorm(0.05,2,1,lower.tail=FALSE) # Question (b)
[1] 3.644854
>rnorm(5,2,1) # Question (c)
[1] 0.7261126 3.1286553 1.0042537 2.8120058 3.9837978
Note that as for the last command, you may not obtain the same result as above because of randomness!