Simulate an inhomogeneous Poisson process:

Mean and variance functions:

Covariance function:

Simulate the arrival process at a small fast-food restaurant if the hourly arrival rates of customers are given by:

Use linear interpolation to obtain the intensity function for the arrival process:

Define an inhomogeneous Poisson process for the arrivals:

Probability that more than 200 customers visit the restaurant during the day:

Simulate the arrival process for a day:

Use simulation to find the effective hourly mean arrival rate:

Define the square of an inhomogeneous Poisson process:

Simulate the process:

Mean and variance for the process slices:

An inhomogeneous Poisson process with Weibull failure rate intensity is known as Weibull Poisson process:

Sample process trajectories:

Use simulation to find the effective mean intensity rate for a day:

Compare to the mean intensity rate given by the integral of the rate function:

InhomogeneousPoissonProcess is a jump process:

An inhomogeneous Poisson process is not weakly stationary:

The mean function is not constant:

An inhomogeneous Poisson process with constant intensity is a PoissonProcess:

Compare univariate slice distributions:

Multi-slice properties:

Some of the simulation methods require a bounded intensity function:

The default "Thinning" method fails:

The inversion method also fails for this intensity function:

The direct method is suitable for an unbounded intensity function, although it may be slow:

Simulate paths from an inhomogeneous Poisson process:

Take a slice at 50 and visualize its distribution:

Plot paths and histogram distribution of the slice distribution at 50: