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Fixed typos.
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cfries committed Jun 3, 2024
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Expand Up @@ -5,7 +5,7 @@ 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
a **inhomogeneous exponential distribution**.
an **inhomogeneous exponential distribution**.

```
@FunctionalInterface
Expand Down Expand Up @@ -51,11 +51,11 @@ 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 inhomogenous exponential distribution with a piece-wise constant intensity.
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

- &Lambda;(t) = &lambda;<sub>0</sub> t for t < t<sub>0</sub>
- &Lambda;(t<sub>i</sub>) = &lambda;<sub>0</sub> (t<sub>0</sub>-0) + &lambda<sub>1</sub> (t<sub>1</sub>-t<sub>0</sub>) + ... + &lambda;<sub>i</sub> (t<sub>i</sub>-t<sub>i-1</sub>)
- &Lambda;(t) = &Lambda;(t<sub>i-1</sub>) + &lambda;<sub>i</sub> (t-t<sub>i-1</sub>) for t<sub>i-1</sub> < t < t<sub>i</sub>
- &Lambda;(t) = &lambda;<sub>0</sub> &middot; t for t < t<sub>0</sub>
- &Lambda;(t<sub>i</sub>) = &lambda;<sub>0</sub> &middot; (t<sub>0</sub>-0) + &lambda;<sub>1</sub> &middot; (t<sub>1</sub>-t<sub>0</sub>) + ... + &lambda;<sub>i</sub> &middot; (t<sub>i</sub>-t<sub>i-1</sub>)
- &Lambda;(t) = &Lambda;(t<sub>i-1</sub>) + &lambda;<sub>i</sub> &middot; (t-t<sub>i-1</sub>) for t<sub>i-1</sub> < t < t<sub>i</sub>

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