137 lines
4.0 KiB
Plaintext
137 lines
4.0 KiB
Plaintext
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---
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sidebar_position: 7
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---
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import { SquiggleEditor } from '@quri/squiggle-components'
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# Squiggle Functions Reference
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## Distributions
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### Normal distribution
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The `normal(mean, sd)` function creates a normal distribution with the given mean
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and standard deviation.
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<SquiggleEditor initialSquiggleString="normal(0, 1)" />
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### Uniform distribution
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The `uniform(low, high)` function creates a uniform distribution between the
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two given numbers:
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<SquiggleEditor initialSquiggleString="uniform(0, 10)" />
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### Lognormal distribution
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The `lognormal(mu, sigma)` returns the log of a normal distribution with parameters
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mu and sigma. The log of lognormal(mu, sigma) is a normal distribution with parameters
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mean mu and standard deviation sigma.
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<SquiggleEditor initialSquiggleString="lognormal(0, 1)" />
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An alternative format is also available. The "to" notation creates a lognormal
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distribution with a 90% confidence interval between the two numbers. We add
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this convinience as lognormal distributions are commonly used in practice
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<SquiggleEditor initialSquiggleString="2 to 10" />
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Furthermore, it's also possible to create a lognormal from it's actual mean
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and standard deviation, using `lognormalFromMeanAndStdDev`:
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<SquiggleEditor initialSquiggleString="lognormalFromMeanAndStdDev(20, 20)" />
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### Beta distribution
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The `beta(a, b)` function creates a beta distribution with parameters a and b:
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<SquiggleEditor initialSquiggleString="beta(20, 20)" />
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### Exponential distribution
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The `exponential(mean)` function creates an exponential distribution with the given
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mean.
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<SquiggleEditor initialSquiggleString="exponential(1)" />
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### The Triangular distribution
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The `triangular(a,b,c)` function creates a triangular distribution with lower
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bound a, mode b and upper bound c:
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<SquiggleEditor initialSquiggleString="triangular(1, 2, 4)" />
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### Multimodal distriutions
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The multimodal function combines 2 or more other distributions to create a weighted
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combination of the two. The first positional arguments represent the distributions
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to be combined, and the last argument is how much to weigh every distribution in the
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combination.
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<SquiggleEditor initialSquiggleString="mm(uniform(0,1), normal(1,1), [0.5, 0.5])" />
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It's possible to create discrete distributions using this method:
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<SquiggleEditor initialSquiggleString="mm(0, 1, [0.2,0.8])" />
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As well as mixed distributions:
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<SquiggleEditor initialSquiggleString="mm(0, 1 to 10, [0.2,0.8])" />
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## Other Functions
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### PDF of a distribution
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The `pdf(distribution, x)` function returns the density of a distribution at the
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given point x:
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<SquiggleEditor initialSquiggleString="pdf(normal(0,1),0)" />
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### Inverse of a distribution
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The `inv(distribution, prob)` gives the value x or which the probability for all values
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lower than x is equal to prob. It is the inverse of `cdf`
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<SquiggleEditor initialSquiggleString="inv(normal(0,1),0.5)" />
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### CDF of a distribution
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The `cdf(distribution,x)` gives the cumulative probability of the distribution
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or all values lower than x. It is the inverse of `inv`:
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<SquiggleEditor initialSquiggleString="cdf(normal(0,1),0)" />
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### Mean of a distribution
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The `mean(distribution)` function gives the mean (expected value) of a distribution:
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<SquiggleEditor initialSquiggleString="mean(normal(5, 10))" />
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### Sampling a distribution
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The `sample(distribution)` samples a given distribution:
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<SquiggleEditor initialSquiggleString="sample(normal(0, 10))" />
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### Exponential Scaling
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The `scaleExp(distribution, factor)` function scales a distribution's PDF exponentially
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in the y axis.
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<SquiggleEditor initialSquiggleString="scaleExp(normal(10, 10), 10)" />
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### Multiply Scaling
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The `scaleMultiply(distribution, factor)` function scales a distribution's PDF by multiplication
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in the y axis.
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<SquiggleEditor initialSquiggleString="scaleMultiply(normal(10, 10), 2)" />
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### Log scaling
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The `scaleLog(distribution, factor)` function scales a distribution's PDF by the log
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function in the y axis
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<SquiggleEditor initialSquiggleString="scaleLog(normal(10, 10), 2)" />
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