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Update prob distributions
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@ -87,12 +87,12 @@ $$0\leq u \leq \sqrt{f\left({v\over u}\right)}$$
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In this method, $f(x)$ doesn't need to be normalized, only the shape of the function is needed. This method was introduced by [Kinderman and Monahan 1977](https://dl.acm.org/doi/pdf/10.1145/355744.355750).
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In this method, $f(x)$ doesn't need to be normalized, only the shape of the function is needed. This method was introduced by [Kinderman and Monahan 1977](https://dl.acm.org/doi/pdf/10.1145/355744.355750).
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Again note how this method allows us to access the range $x=0$ to $\infty$, since the ratio $v/u\rightarrow \infty$ for $u\rightarrow 0$.
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Again note how this method allows us to access the range $x=0$ to $\infty$, since the ratio $v/u\rightarrow \infty$ for $u\rightarrow 0$.
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```{admonition} Exercise:
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```{admonition} Exercise 1
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Implement these three methods for the exponential distribution and check that they work by comparing a histogram of your $x$ values with the analytic function.
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Implement these three methods for the exponential distribution and check that they work by comparing a histogram of your $x$ values with the analytic function.
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```
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```
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```{admonition} Exercise:
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```{admonition} Exercise 2
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Try implementing one of the following:
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Try implementing one of the following:
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- Lorentzian distribution using transformation method
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- Lorentzian distribution using transformation method
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@ -5,7 +5,7 @@
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"id": "6d46a72f",
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"id": "6d46a72f",
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"metadata": {},
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"metadata": {},
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"source": [
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"source": [
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"# Sampling probability distributions Part 1"
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"# Probability distributions Exercise 1"
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]
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]
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},
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},
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{
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{
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@ -260,7 +260,7 @@
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"name": "python",
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"name": "python",
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"nbconvert_exporter": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"pygments_lexer": "ipython3",
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"version": "3.11.4"
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"version": "3.11.5"
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}
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}
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},
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},
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"nbformat": 4,
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"nbformat": 4,
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