Minor additions of delta distribution
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Ozzie Gooen
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18af09ab04
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8147c5ad60
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@ -134,6 +134,7 @@ mx(forecast, forecast_if_completely_wrong, [1-chance_completely_wrong, chance_co
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`normal(mean:number, standardDeviation:number)`
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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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@ -168,9 +169,13 @@ Creates a [log-normal distribution](https://en.wikipedia.org/wiki/Log-normal_dis
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[Wikipedia](https://en.wikipedia.org/wiki/Log-normal_distribution)
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<details>
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<summary>❓ Understanding <bold>mu</bold> and <bold>sigma</bold></summary>
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<summary>
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❓ Understanding <bold>mu</bold> and <bold>sigma</bold>
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</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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The log of `lognormal(mu, sigma)` is a normal distribution with mean `mu`
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and standard deviation `sigma`. For example, these two distributions are
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identical:
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</p>
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<SquiggleEditor
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initialSquiggleString={`normalMean = 10
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@ -184,7 +189,8 @@ logOfLognormal = log(lognormal(normalMean, normalStdDev))
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`uniform(low:number, high:number)`
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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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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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### Arguments
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@ -194,16 +200,52 @@ Creates a [uniform distribution](https://en.wikipedia.org/wiki/Uniform_distribut
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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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While uniform distributions are very simple to understand, we find it rare
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to find uncertainties that actually look like this. Before using a uniform
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distribution, think hard about if you are really 100% confident that the
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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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One good example of a uniform distribution uncertainty would be clear
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physical limitations. You might have complete complete uncertainty on what
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time of day an event will occur, but can say with 100% confidence it will
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happen between the hours of 0:00 and 24:00.
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</p>
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</Admonition>
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## Delta
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`delta(value:number)`
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Creates a discrete distribution with all of its probability mass at point `value`.
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Numbers are often cast into delta distributions automatically. For example, in the function,
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`mixture(1,2,normal(5,2))`, the first two arguments will get converted into delta distributions
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with values at 1 and 2. Therefore, `mixture(1,2,normal(5,2))` is the same as `mixture(delta(1), delta(2),normal(5,2))`
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<Tabs>
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<TabItem value="ex1" label="delta(3)" default>
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<SquiggleEditor initialSquiggleString="delta(3)" />
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</TabItem>
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<TabItem value="ex3" label="mixture(1,3,5)">
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<SquiggleEditor initialSquiggleString="mixture(1,3,5)" />
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</TabItem>
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<TabItem value="ex2" label="normal(5,2) * 6">
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<SquiggleEditor initialSquiggleString="normal(5,2) * 6" />
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</TabItem>
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<TabItem value="ex4" label="normal(5,2) .* 6">
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<SquiggleEditor initialSquiggleString="normal(5,2) .* 6" />
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</TabItem>
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</Tabs>
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### Arguments
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- `value`: Number
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## Beta
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``beta(alpha:number, beta:number)``
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`beta(alpha:number, beta:number)`
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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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@ -232,7 +274,9 @@ Creates a [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution) w
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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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Squiggle struggles to show beta distributions when either alpha or beta are
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below 1.0. This is because the tails at ~0.0 and ~1.0 are very high. Using a
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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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@ -255,24 +299,26 @@ Creates a [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution) w
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## Exponential
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``exponential(rate:number)``
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`exponential(rate:number)`
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Creates an [exponential distribution](https://en.wikipedia.org/wiki/Exponential_distribution) with the given rate.
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<SquiggleEditor initialSquiggleString="exponential(4)" />
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### Arguments
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- `rate`: Number greater than zero
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## Triangular distribution
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``triangular(low:number, mode:number, high:number)``
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`triangular(low:number, mode:number, high:number)`
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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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### Arguments
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- `low`: Number
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- `mode`: Number greater than `low`
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- `high`: Number greater than `mode`
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@ -281,11 +327,12 @@ Creates a [triangular distribution](https://en.wikipedia.org/wiki/Triangular_dis
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## FromSamples
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``fromSamples(samples:number[])``
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`fromSamples(samples:number[])`
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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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### Arguments
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- `samples`: An array of at least 5 numbers.
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