Create Poisson process...

A command to create a PointProcess object that represents a Poisson process.

A Poisson process is a stationary point process with a fixed density λ, which means that there are, on the average, λ events per second.

Settings

Start time (s)
tmin, the beginning of the time domain, in seconds.
End time (s)
tmax, the end of the time domain, in seconds.
Density (Hz)
the average number of points per second.

Algorithm

First, the number of points N in the time domain is determined. Its expectation value is

λ = (tmaxtmin) · density

but its actual value is taken from the Poisson distribution:

p(n) = (λn / n!) eλ

Then, N points are computed throughout the time domain, according to a uniform distribution:

p(t) = 1 / (tmaxtmin) for t ∈ [tmin, tmax]
p(t) = 0 outside [tmin, tmax]

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© ppgb, October 5, 2004