numerical-methods-inhomogeneousexponentialrandomnumbergenerator-exercise

This exercise is related to random number generation:

Random Number Generation: ICDF Method for Inhomogeneous Exponential Distribution

1. Implement a class that implements the interface DoubleSupplier of the package java.util.function.DoubleSupplier that generates a sequence of random drawings of an inhomogeneous exponential distribution with piece-wise constant intensities (see below how we provide the piece-wise constant intensities).

@FunctionalInterface
public interface DoubleSupplier {

    /**
     * Gets a result.
     *
     * @return a result
     */
    double getAsDouble();
}

2. When done with 1) implement the method createRandomNumberGeneratorInhomogenousExponential of the class InhomogenousExponentialAssignmentSolution, such that it allows to create an object of the class you have implemented in 1).

public DoubleSupplier createRandomNumberGeneratorInhomogenousExponential(RandomNumberGenerator1D uniformSequence, double[] times, double[] intensities)

Note: The arguments times and intensities that are provided to you have the following interpretation:

• The length of the array intensities is times.length + 1.
• intensities[0] is the intensity for the time period from 0 to times[0].
• intensities[i] is the intensity for the time period from times[i-1] to times[i].
• intensities[n] is the intensity for the time period from times[n-1] to Double.INFINITY.

where n = intensities.length-1, i.e., n = times.length.

A class like InhomogenousExponentialAssignmentSolution is called a Factory, because it allows to create objects. It allows us to create an object of your class, without knowing the name of your class. We will use this method to test your implementation.

Hint: This is a trivial task. If your class in 1) is named RandomNumberGeneratorInhomogenousExponential and if it has a constructor RandomNumberGeneratorInhomogenousExponential(RandomNumberGenerator1D uniformSequence, double[] times, double[] intensities), then the body of the implementation of the factory class is just

public DoubleSupplier createRandomNumberGeneratorInhomogenousExponential(RandomNumberGenerator1D uniformSequence, double[] times, double[] intensities) 	{
	return new RandomNumberGeneratorInhomogenousExponential(uniformSequence, times, intensities);
}

You can test your implementation by running the unit test in src/test/java.

Main Task

The main task of this exercise is to provide the inversion of the distribution function of an inhomogeneous exponential distribution with a piece-wise constant intensity.

The most involved step is the inversion of the function t ↦ Λ(t), where

• Λ(t) = λ₀ · t for t < t₀
• Λ(t_i) = λ₀ · (t₀-0) + λ₁ · (t₁-t₀) + ... + λ_i · (t_i-t_i-1)
• Λ(t) = Λ(t_i-1) + λ_i · (t-t_i-1) for t_i-1 < t < t_i