rand — Random Values

$\begin{rail} Random : 'rand' '(' ( () \vert ( Scalar ',' Scalar ) \vert ( '''d... ... ',' Scalar ) \vert ( '''uniform''' ',' Scalar ',' Scalar ) ) ')' ; \end{rail}$
rand has two distinct forms. The first form is used to set the distribution that is used to generate random values. The second form actually generates the values. We will look at each form in turn.

β distribution. If the first scalar argument is a and the second scalar argument is b, then the density of the distribution is

$\displaystyle {\frac{{x^{a-1} (1-x)^{b-1}}}{{B(a,b)}}}$ $\displaystyle \mbox{for $0 < x < 1$}$
where B(a, b) is the binomial distribution.
Binomial distribution. The first scalar argument specifies the number of trials, and the second scalar argument specifies the probability of an event occuring in a trial.
χ² distribution. The scalar argument specifies the number of degrees of freedom.
Default distribution. The default distribution is a uniform distribution between 0 and 1.
Exponential distribution. The scalar argument specifies the mean of the distribution.
$\cal {F}$ distribution. The first scalar argument specifies the degrees of freedom present in the numerator, and the second scalar argument specifies the degrees of freedom in the denominator.
Γ distribution. If the first scalar argument is a, and the second scalar argument is r, then the density of the distribution is:

$\displaystyle {\frac{{a^{r}}}{{\Gamma(r)}}}$ x^r-1e^-ax
Non-central χ² distribution The first scalar argument specifies the number of degrees of freedom, and the second scalar argument specifies the non-centrality.
Non-central $\cal {F}$ distribution. The first scalar argument specifies the degrees of freedom present in the numerator, the second scalar argument specifies the degrees of freedom in the denominator, and the third scalar argument specifies the non-centrality.
Normal distribution. The first scalar argument specifies the mean, and the second scalar argument specifies the standard distribution.
Poisson distribution. The scalar argument specifies the mean of the distribution.
Uniform distribution. The first scalar argument specifies the lower limit, and the second scalar argument specifies the upper limit.

The second form of the rand function is used to produce random variables from whatever distribution is actually selected at the time. If you supply no arguments, then a random scalar is returned. If you supply two scalar arguments, then a matrix is returned. The first argument specifies the number of rows, and the second argument specifies the number of columns. In addition, you can supply a matrix argument, which must have two elements, where the first is the number of rows, and the second is the number of columns. This is intended for use with the size function. If srand is not used to set the seed value, each session will produce the same results.

Subsections

- - Example