Starting to pull out distributions for more specialized documentation
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Ozzie Gooen
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@ -26,7 +26,7 @@ If both values are above zero, a `lognormal` distribution is used. If not, a `no
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lognormal distribution with 5th and 95th percentiles at 5 and 10.
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<SquiggleEditor initialSquiggleString="5 to 10" />
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</TabItem>
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<TabItem value="ex3" label="to(5,10)" default>
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<TabItem value="ex3" label="to(5,10)">
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`5 to 10` does the same thing as `to(5,10)`.
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<SquiggleEditor initialSquiggleString="to(5,10)" />
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</TabItem>
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@ -45,7 +45,7 @@ If both values are above zero, a `lognormal` distribution is used. If not, a `no
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### Arguments
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- `5thPercentile`: Float
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- `95thPercentile`: Float
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- `95thPercentile`: Float, greater than `5thPercentile`
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<Admonition type="tip" title="Tip">
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<p>
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@ -77,10 +77,10 @@ The `mixture` mixes combines multiple distributions to create a mixture. You can
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<TabItem value="ex1" label="Simple" default>
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<SquiggleEditor initialSquiggleString="mixture(1 to 2, 5 to 8, 9 to 10)" />
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</TabItem>
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<TabItem value="ex2" label="With Weights" default>
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<TabItem value="ex2" label="With Weights">
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<SquiggleEditor initialSquiggleString="mixture(1 to 2, 5 to 8, 9 to 10, [0.1, 0.1, 0.8])" />
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</TabItem>
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<TabItem value="ex3" label="With Continuous and Discrete Inputs" default>
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<TabItem value="ex3" label="With Continuous and Discrete Inputs">
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<SquiggleEditor initialSquiggleString="mixture(1 to 5, 8 to 10, 1, 3, 20)" />
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</TabItem>
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</Tabs>
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@ -137,11 +137,12 @@ mx(forecast, forecast_if_completely_wrong, [1-chance_completely_wrong, chance_co
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`normal(mean:float, standardDeviation:float)`
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Creates a [normal distribution](https://en.wikipedia.org/wiki/Normal_distribution) with the given mean and standard deviation.
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<Tabs>
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<TabItem value="ex1" label="normal(5,1)" default>
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<SquiggleEditor initialSquiggleString="normal(5, 1)" />
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</TabItem>
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<TabItem value="ex2" label="normal(10m, 10m)" default>
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<TabItem value="ex2" label="normal(100000000000, 100000000000)">
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<SquiggleEditor initialSquiggleString="normal(100000000000, 100000000000)" />
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</TabItem>
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</Tabs>
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@ -151,14 +152,14 @@ mx(forecast, forecast_if_completely_wrong, [1-chance_completely_wrong, chance_co
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- `mean`: Float
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- `standard deviation`: Float greater than zero
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[Wikipedia entry](https://en.wikipedia.org/wiki/Normal_distribution)
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[Wikipedia](https://en.wikipedia.org/wiki/Normal_distribution)
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## Log-normal
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The log of `lognormal(mu, sigma)` is a normal distribution with mean `mu` and standard deviation `sigma`.
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`lognormal(mu: float, sigma: float)`
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Creates a [log-normal distribution](https://en.wikipedia.org/wiki/Log-normal_distribution) with the given mu and sigma.
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<SquiggleEditor initialSquiggleString="lognormal(0, 0.7)" />
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### Arguments
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@ -168,85 +169,124 @@ The log of `lognormal(mu, sigma)` is a normal distribution with mean `mu` and st
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[Wikipedia](https://en.wikipedia.org/wiki/Log-normal_distribution)
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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 convenience as lognormal distributions are commonly used in practice.
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### Argument Alternatives
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`Mu` and `sigma` can be difficult to directly reason about. Because of this complexity, we recommend typically using the <a href="#to">to</a> syntax.
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<SquiggleEditor initialSquiggleString="2 to 10" />
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#### Future feature:
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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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TODO: interpreter/parser doesn't provide this in current `develop` branch
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<SquiggleEditor initialSquiggleString="lognormalFromMeanAndStdDev(20, 10)" />
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#### Validity
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- `sigma > 0`
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- In `x to y` notation, `x < y`
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<details>
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<summary>❓ Understanding <bold>mu</bold> and <bold>sigma</bold></summary>
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<p>
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The log of `lognormal(mu, sigma)` is a normal distribution with mean `mu` and standard deviation `sigma`. For example, these two distributions are identical:
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</p>
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<SquiggleEditor
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initialSquiggleString={`normalMean = 10
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normalStdDev = 2
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logOfLognormal = log(lognormal(normalMean, normalStdDev))
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[logOfLognormal, normal(normalMean, normalStdDev)]`}
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/>
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</details>
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## Uniform
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`normal(low:float, high:float)`
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`uniform(low:float, high:float)`
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<Tabs>
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<TabItem value="ex1" label="uniform(3,7)" default>
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Creates a [uniform distribution](https://en.wikipedia.org/wiki/Uniform_distribution_(continuous)) with the given low and high values.
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<SquiggleEditor initialSquiggleString="uniform(3,7)" />
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</TabItem>
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<TabItem value="ex2" label="invalid: uniform(7,5)" default>
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<SquiggleEditor initialSquiggleString="uniform(7,5)" />
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</TabItem>
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</Tabs>
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### Arguments
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- `low`: Float
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- `high`: Float greater than `low`
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<Admonition type="caution" title="Caution">
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<p>
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While uniform distributions are very simple to understand, we find it rare to find uncertainties that actually look like this. Before using a uniform distribution, think hard about if you are really 100% confident that the paramater will not wind up being just outside the stated boundaries.
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</p>
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<p>
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One good example of a uniform distribution uncertainty would be clear physical limitations. You might have complete complete uncertainty on what time of day an event will occur, but can say with 100% confidence it will happen between the hours of 0:00 and 24:00.
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</p>
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</Admonition>
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## Beta
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``beta(alpha:float, beta:float)``
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The `beta(a, b)` function creates a beta distribution with parameters `a` and `b`:
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Creates a [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution) with the given `alpha` and `beta` values. For a good summary of the beta distribution, see [this explanation](https://stats.stackexchange.com/a/47782) on Stack Overflow.
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<Tabs>
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<TabItem value="ex1" label="beta(10, 20)" default>
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<SquiggleEditor initialSquiggleString="beta(10,20)" />
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</TabItem>
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<TabItem value="ex2" label="beta(1000, 1000)" >
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<SquiggleEditor initialSquiggleString="beta(1000, 2000)" />
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</TabItem>
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<TabItem value="ex3" label="beta(1, 10)" >
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<SquiggleEditor initialSquiggleString="beta(1, 10)" />
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</TabItem>
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<TabItem value="ex4" label="beta(10, 1)" >
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<SquiggleEditor initialSquiggleString="beta(10, 1)" />
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</TabItem>
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<TabItem value="ex5" label="beta(0.8, 0.8)" >
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<SquiggleEditor initialSquiggleString="beta(0.8, 0.8)" />
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</TabItem>
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</Tabs>
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#### Validity
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### Arguments
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- `a > 0`
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- `b > 0`
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- Empirically, we have noticed that numerical instability arises when `a < 1` or `b < 1`
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- `alpha`: Float greater than zero
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- `beta`: Float greater than zero
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<Admonition type="caution" title="Caution with small numbers">
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<p>
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Squiggle struggles to show beta distributions when either alpha or beta are below 1.0. This is because the tails at ~0.0 and ~1.0 are very high. Using a log scale for the y-axis helps here.
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</p>
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<details>
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<summary>Examples</summary>
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<Tabs>
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<TabItem value="ex1" label="beta(0.3, 0.3)" default>
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<SquiggleEditor initialSquiggleString="beta(0.3, 0.3)" />
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</TabItem>
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<TabItem value="ex2" label="beta(0.5, 0.5)">
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<SquiggleEditor initialSquiggleString="beta(0.5, 0.5)" />
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</TabItem>
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<TabItem value="ex3" label="beta(0.8, 0.8)">
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<SquiggleEditor initialSquiggleString="beta(.8,.8)" />
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</TabItem>
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<TabItem value="ex4" label="beta(0.9, 0.9)">
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<SquiggleEditor initialSquiggleString="beta(.9,.9)" />
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</TabItem>
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</Tabs>
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</details>
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</Admonition>
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## Exponential
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The `exponential(rate)` function creates an exponential distribution with the given
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rate.
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``exponential(rate:float)``
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<SquiggleEditor initialSquiggleString="exponential(1.11)" />
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Creates an [exponential distribution](https://en.wikipedia.org/wiki/Exponential_distribution) with the given rate.
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#### Validity
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<SquiggleEditor initialSquiggleString="exponential(4)" />
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- `rate > 0`
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### Arguments
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- `rate`: Float greater than zero
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## 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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``triangular(low:float, mode:float, high:float)``
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Creates a [triangular distribution](https://en.wikipedia.org/wiki/Triangular_distribution) with the given low, mode, and high values.
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#### Validity
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- `a < b < c`
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### Arguments
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- `low`: Float
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- `mode`: Float greater than `low`
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- `high`: Float greater than `mode`
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<SquiggleEditor initialSquiggleString="triangular(1, 2, 4)" />
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### Scalar (constant dist)
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## FromSamples
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Squiggle, when the context is right, automatically casts a float to a constant distribution.
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## `fromSamples`
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The last distribution constructor takes an array of samples and constructs a sample set distribution.
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Creates a sample set distribution using an array of samples.
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<SquiggleEditor initialSquiggleString="fromSamples([1,2,3,4,6,5,5,5])" />
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@ -5,110 +5,6 @@ sidebar_position: 7
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import { SquiggleEditor } from "../../src/components/SquiggleEditor";
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## Inventory distributions
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We provide starter distributions, computed symbolically.
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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(5, 1)" />
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#### Validity
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- `sd > 0`
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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(3, 7)" />
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#### Validity
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- `low < high`
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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 mean `mu` and standard deviation `sigma`.
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<SquiggleEditor initialSquiggleString="lognormal(0, 0.7)" />
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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 convenience as lognormal distributions are commonly used in practice.
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<SquiggleEditor initialSquiggleString="2 to 10" />
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#### Future feature:
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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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TODO: interpreter/parser doesn't provide this in current `develop` branch
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<SquiggleEditor initialSquiggleString="lognormalFromMeanAndStdDev(20, 10)" />
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#### Validity
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- `sigma > 0`
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- In `x to y` notation, `x < y`
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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(10, 20)" />
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#### Validity
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- `a > 0`
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- `b > 0`
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- Empirically, we have noticed that numerical instability arises when `a < 1` or `b < 1`
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### Exponential distribution
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The `exponential(rate)` function creates an exponential distribution with the given
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rate.
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<SquiggleEditor initialSquiggleString="exponential(1.11)" />
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#### Validity
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- `rate > 0`
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### 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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#### Validity
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- `a < b < c`
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<SquiggleEditor initialSquiggleString="triangular(1, 2, 4)" />
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### Scalar (constant dist)
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Squiggle, when the context is right, automatically casts a float to a constant distribution.
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## `fromSamples`
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The last distribution constructor takes an array of samples and constructs a sample set distribution.
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<SquiggleEditor initialSquiggleString="fromSamples([1,2,3,4,6,5,5,5])" />
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#### Validity
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For `fromSamples(xs)`,
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- `xs.length > 5`
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- Strictly every element of `xs` must be a number.
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## Operating on distributions
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Here are the ways we combine distributions.
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