rndBinomial#

Purpose#

Computes binomial pseudo-random numbers with the choice of underlying random number generator.

Format#

x = rndBinomial(r, c, trials, prob)#

{ x, newstate } = rndBinomial(r, c, trials, prob, state)

Parameters:

r (scalar) – number of rows of resulting matrix.
c (scalar) – number of columns of resulting matrix.
trials (matrix or vector or scalar) – the number of trials, scalar or ExE conformable with r and c.
prob (matrix or vector or scalar) – the probability of success of each trial, scalar or ExE conformable with r and c.
state (scalar or opaque vector) –
Optional argument.

scalar case

state = starting seed value only. If -1, GAUSS computes the starting seed based on the system clock.

opaque vector case

state = the state vector returned from a previous call to one of the rnd random number functions.

Returns:

x (RxC matrix) – binomially distributed random numbers.
newstate (Opaque vector) – the updated state.

Examples#

Basic usage#

// Set seed for repeatable random numbers
rndseed 7345;

// Simulate the number of successes from 1024 trials,
// each of which have a 40% chance of success, 3 times
n = 1024;
p = 0.4;
k = rndBinomial(3, 1, n, p);

After the code above, k should equal:

413
390
427

Pass seed and return state vector#

// Simulate the number of successes from 1024 trials,
// each of which have a 40% chance of success, 3 times
n = 1024;
p = 0.4;

// Pass in seed as optional final input argument
// and return state vector as second output
{ k, state } = rndBinomial(3, 1, n, p, 7345);

After the code above, k should equal:

413
390
427

Technical Notes#

The default generator for func:rndBinomial is the SFMT Mersenne-Twister 19937. You can specify a different underlying random number generator with the function rndCreateState().

Remarks#

The properties of the pseudo-random numbers in x are:

\[\begin{split}\mu = np\\ \sigma^2 = np(1 - p)\\ \text{pmf } = {{n}\choose{k}}p^k(1 - p)^{n - k}\\ \text{ }\\ \text{n = number of trials}\\ \text{p = probability of success}\\ \text{k = number of successes}\end{split}\]

r and c will be truncated to integers if necessary.