`exprnd` — Exponentially-distributed random numbers with mean mu.

exprnd draws pseudorandom samples from the exponential distribution with mean mu (equivalently, rate parameter lambda = 1/mu). It is part of the Statistics and Machine Learning Toolbox family in MATLAB and Octave's statistics package. RunMat implements it via inverse transform sampling: r = -mu * ln(U) where U ~ Uniform(0, 1).

How `exprnd` works

exprnd(mu) returns a scalar double drawn from Exp(mu).
exprnd(mu, n) returns an n × n matrix of samples.
exprnd(mu, m, n) returns an m × n matrix of samples.
exprnd(mu, sz) accepts a size vector and returns an array with shape sz.
mu must be a positive scalar; exprnd errors if mu <= 0.
All outputs are double precision regardless of input type.

Examples

Single sample from Exp(2)

rng(0);
r = exprnd(2)

Matrix of arrival times for a Poisson process (lambda = 2)

rng(0);
lambda = 2;
intervals = exprnd(1/lambda, 1, 5)

M/M/1 queueing simulation fragment

rng(0);
lambda = 2; mu_svc = 2.5; Tsim = 100;
t = 0; arrivals = 0;
while t < Tsim
    t = t + exprnd(1/lambda);
    arrivals = arrivals + 1;
end
arrivals

Specifying dimensions with a size vector

rng(0);
T = exprnd(1, [2 3])

FAQ

What is the relationship between mu and lambda?

The exponential distribution can be parameterised by its mean mu or its rate lambda. They are reciprocals: mu = 1/lambda. exprnd(mu) is equivalent to exprnd(1/lambda).

What is the workaround if exprnd is unavailable?

exprnd(mu) is mathematically equivalent to -mu * log(rand()). You can substitute -log(rand())/lambda inline until exprnd is available.

Why must mu be positive?

A non-positive mean is undefined for the exponential distribution. exprnd raises an error if mu <= 0 to catch common parameter mistakes early.

What use cases does exprnd support?

Common uses include queueing theory (M/M/1, M/G/1 inter-arrival and service times), reliability engineering (time-to-failure models), Poisson process simulation, and Monte Carlo sampling.

Does exprnd fuse with other operations?

No. Random generation is excluded from fusion planning to preserve statistical properties.

How do I control reproducibility?

Use rng before calling exprnd to seed the global generator.

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how exprnd works, line by line, in Rust.

View exprnd.rs on GitHub
Learn how the runtime works
Found a bug? Open an issue with a minimal reproduction.

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exprnd — Exponentially-distributed random numbers with mean mu.

How exprnd works