rndLogNorm#

Purpose#

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

Format#

x = rndLogNorm(r, c, mu, sigma)#

{ x, newstate } = rndLogNorm(r, c, mu, sigma, state)

Parameters:

r (scalar) – number of rows of resulting matrix.
c (scalar) – number of columns of resulting matrix.
mu (matrix or vector or scalar) – mean, scalar or ExE conformable matrix with r and c.
sigma (matrix or vector or scalar) – standard deviation, scalar or ExE conformable matrix 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) – lognormal distributed random numbers.
newstate (Opaque vector) – the updated state.

Remarks#

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

\[ \begin{align}\begin{aligned}\begin{split}E(x) = exp(\mu - 0.5*\sigma^2)\\\end{split}\\Var(x) = (exp(\sigma^2) - 1) * exp(2*\mu + \sigma^2)\end{aligned}\end{align} \]

r and c will be truncated to integers if necessary.