Minor additions of delta distribution

2022-05-01 15:04:00 -04:00 · 2022-05-01 15:04:00 -04:00 · 8147c5ad60
commit 8147c5ad60
parent 18af09ab04
1 changed files with 84 additions and 37 deletions
--- a/packages/website/docs/Features/Distributions.mdx
+++ b/packages/website/docs/Features/Distributions.mdx
@ -134,6 +134,7 @@ mx(forecast, forecast_if_completely_wrong, [1-chance_completely_wrong, chance_co
 `normal(mean:number, standardDeviation:number)`

 Creates a [normal distribution](https://en.wikipedia.org/wiki/Normal_distribution) with the given mean and standard deviation.
+
 <Tabs>
  <TabItem value="ex1" label="normal(5,1)" default>
    <SquiggleEditor initialSquiggleString="normal(5, 1)" />
@ -168,23 +169,28 @@ Creates a [log-normal distribution](https://en.wikipedia.org/wiki/Log-normal_dis
 [Wikipedia](https://en.wikipedia.org/wiki/Log-normal_distribution)

 <details>
-  <summary>❓ Understanding <bold>mu</bold> and <bold>sigma</bold></summary>
+  <summary>
+    ❓ Understanding <bold>mu</bold> and <bold>sigma</bold>
+  </summary>
  <p>
-    The log of `lognormal(mu, sigma)` is a normal distribution with mean `mu` and standard deviation `sigma`. For example, these two distributions are identical:
+    The log of `lognormal(mu, sigma)` is a normal distribution with mean `mu`
+    and standard deviation `sigma`. For example, these two distributions are
+    identical:
  </p>
-<SquiggleEditor
+  <SquiggleEditor
    initialSquiggleString={`normalMean = 10
 normalStdDev = 2
 logOfLognormal = log(lognormal(normalMean, normalStdDev))
 [logOfLognormal, normal(normalMean, normalStdDev)]`}
-/>
+  />
 </details>

 ## Uniform

 `uniform(low:number, high:number)`

-Creates a [uniform distribution](https://en.wikipedia.org/wiki/Uniform_distribution_(continuous)) with the given low and high values.
+Creates a [uniform distribution](<https://en.wikipedia.org/wiki/Uniform_distribution_(continuous)>) with the given low and high values.
+
 <SquiggleEditor initialSquiggleString="uniform(3,7)" />

 ### Arguments
@ -194,16 +200,52 @@ Creates a [uniform distribution](https://en.wikipedia.org/wiki/Uniform_distribut

 <Admonition type="caution" title="Caution">
  <p>
-    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.
+    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.
  </p>

  <p>
-    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. 
+    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.
  </p>
 </Admonition>

+## Delta
+
+`delta(value:number)`
+
+Creates a discrete distribution with all of its probability mass at point `value`.
+
+Numbers are often cast into delta distributions automatically. For example, in the function, 
+`mixture(1,2,normal(5,2))`, the first two arguments will get converted into delta distributions 
+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))`
+
+<Tabs>
+  <TabItem value="ex1" label="delta(3)" default>
+    <SquiggleEditor initialSquiggleString="delta(3)" />
+  </TabItem>
+  <TabItem value="ex3" label="mixture(1,3,5)">
+    <SquiggleEditor initialSquiggleString="mixture(1,3,5)" />
+  </TabItem>
+  <TabItem value="ex2" label="normal(5,2) * 6">
+    <SquiggleEditor initialSquiggleString="normal(5,2) * 6" />
+  </TabItem>
+  <TabItem value="ex4" label="normal(5,2) .* 6">
+    <SquiggleEditor initialSquiggleString="normal(5,2) .* 6" />
+  </TabItem>
+</Tabs>
+
+### Arguments
+
+- `value`: Number
+
 ## Beta
-``beta(alpha:number, beta:number)``  
+
+`beta(alpha:number, beta:number)`

 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.

@ -211,16 +253,16 @@ Creates a [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution) w
  <TabItem value="ex1" label="beta(10, 20)" default>
    <SquiggleEditor initialSquiggleString="beta(10,20)" />
  </TabItem>
-  <TabItem value="ex2" label="beta(1000, 1000)" >
+  <TabItem value="ex2" label="beta(1000, 1000)">
    <SquiggleEditor initialSquiggleString="beta(1000, 2000)" />
  </TabItem>
-  <TabItem value="ex3" label="beta(1, 10)" >
+  <TabItem value="ex3" label="beta(1, 10)">
    <SquiggleEditor initialSquiggleString="beta(1, 10)" />
  </TabItem>
-  <TabItem value="ex4" label="beta(10, 1)" >
+  <TabItem value="ex4" label="beta(10, 1)">
    <SquiggleEditor initialSquiggleString="beta(10, 1)" />
  </TabItem>
-  <TabItem value="ex5" label="beta(0.8, 0.8)" >
+  <TabItem value="ex5" label="beta(0.8, 0.8)">
    <SquiggleEditor initialSquiggleString="beta(0.8, 0.8)" />
  </TabItem>
 </Tabs>
@ -232,11 +274,13 @@ Creates a [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution) w

 <Admonition type="caution" title="Caution with small numbers">
  <p>
-    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.
+    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.
  </p>
-<details>
+  <details>
    <summary>Examples</summary>
-<Tabs>
+    <Tabs>
      <TabItem value="ex1" label="beta(0.3, 0.3)" default>
        <SquiggleEditor initialSquiggleString="beta(0.3, 0.3)" />
      </TabItem>
@ -249,30 +293,32 @@ Creates a [beta distribution](https://en.wikipedia.org/wiki/Beta_distribution) w
      <TabItem value="ex4" label="beta(0.9, 0.9)">
        <SquiggleEditor initialSquiggleString="beta(.9,.9)" />
      </TabItem>
-</Tabs>
-</details>
+    </Tabs>
+  </details>
 </Admonition>

 ## Exponential

-``exponential(rate:number)``
+`exponential(rate:number)`

 Creates an [exponential distribution](https://en.wikipedia.org/wiki/Exponential_distribution) with the given rate.

 <SquiggleEditor initialSquiggleString="exponential(4)" />

 ### Arguments
+
 - `rate`: Number greater than zero

 ## Triangular distribution

-``triangular(low:number, mode:number, high:number)``
+`triangular(low:number, mode:number, high:number)`

 Creates a [triangular distribution](https://en.wikipedia.org/wiki/Triangular_distribution) with the given low, mode, and high values.

 #### Validity

 ### Arguments
+
 - `low`: Number
 - `mode`: Number greater than `low`
 - `high`: Number greater than `mode`
@ -281,11 +327,12 @@ Creates a [triangular distribution](https://en.wikipedia.org/wiki/Triangular_dis

 ## FromSamples

-``fromSamples(samples:number[])``
+`fromSamples(samples:number[])`

 Creates a sample set distribution using an array of samples.

 <SquiggleEditor initialSquiggleString="fromSamples([1,2,3,4,6,5,5,5])" />

 ### Arguments
+
 - `samples`: An array of at least 5 numbers.