86 lines
3.1 KiB
Markdown
86 lines
3.1 KiB
Markdown
---
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sidebar_position: 10
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title: Danger
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---
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The Danger library contains newer experimental functions which are less stable than Squiggle as a whole. Beware: their name, behavior, namespace or existence may change at any time.
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### laplace
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```js
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Danger.laplace: (number, number) => number
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```
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Calculates the probability implied by [Laplace's rule of succession](https://en.wikipedia.org/wiki/Rule_of_succession)
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```js
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trials = 10
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successes = 1
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Danger.laplace(trials, successes) // (successes + 1) / (trials + 2) = 2 / 12 = 0.1666
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```
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### factorial
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```js
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Danger.factorial: (number) => number
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```
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Returns the factorial of a number
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### choose
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```js
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Danger.choose: (number, number) => number
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```
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`Danger.choose(n,k)` returns `factorial(n) / (factorial(n - k) *.factorial(k))`, i.e., the number of ways you can choose k items from n choices, without repetition. This function is also known as the [binomial coefficient](https://en.wikipedia.org/wiki/Binomial_coefficient).
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### binomial
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```js
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Danger.binomial: (number, number, number) => number
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```
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`Danger.binomial(n, k, p)` returns `choose((n, k)) * pow(p, k) * pow(1 - p, n - k)`, i.e., the probability that an event of probability p will happen exactly k times in n draws.
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### integrateFunctionBetweenWithNumIntegrationPoints
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```js
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Danger.integrateFunctionBetweenWithNumIntegrationPoints: (number => number, number, number, number) => number
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```
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`Danger.integrateFunctionBetweenWithNumIntegrationPoints(f, min, max, numIntegrationPoints)` integrates the function `f` between `min` and `max`, and computes `numIntegrationPoints` in between to do so.
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Note that the function `f` has to take in and return numbers. To integrate a function which returns distributios, use:
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```js
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auxiliaryF(x) = mean(f(x))
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Danger.integrateFunctionBetweenWithNumIntegrationPoints(auxiliaryF, min, max, numIntegrationPoints)
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```
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### integrateFunctionBetweenWithEpsilon
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```js
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Danger.integrateFunctionBetweenWithEpsilon: (number => number, number, number, number) => number
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```
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`Danger.integrateFunctionBetweenWithEpsilon(f, min, max, epsilon)` integrates the function `f` between `min` and `max`, and uses an interval of `epsilon` between integration points when doing so. This makes its runtime less predictable than `integrateFunctionBetweenWithNumIntegrationPoints`, because runtime will not only depend on `epsilon`, but also on `min` and `max`.
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Same caveats as `integrateFunctionBetweenWithNumIntegrationPoints` apply.
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### optimalAllocationGivenDiminishingMarginalReturnsForManyFunctions
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```js
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Danger.optimalAllocationGivenDiminishingMarginalReturnsForManyFunctions: (array<number => number>, number, number) => number
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```
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`Danger.optimalAllocationGivenDiminishingMarginalReturnsForManyFunctions([f1, f2], funds, approximateIncrement)` computes the optimal allocation of $`funds` between `f1` and `f2`. For the answer given to be correct, `f1` and `f2` will have to be decreasing, i.e., if `x > y`, then `f_i(x) < f_i(y)`.
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Example:
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```js
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Danger.optimalAllocationGivenDiminishingMarginalReturnsForManyFunctions({|x| 20-x}, {|y| 10}, 100, 0.01)
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```
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Note also that the array ought to have more than one function in it. |