---
sidebar_position: 2
title: Distribution
---
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<TOCInline toc={toc} />

## Creation

### Normal Distribution

**Definitions**

```javascript
normal(frValueDistOrNumber, frValueDistOrNumber);
```

```javascript
normal(dict<{p5: frValueDistOrNumber, p95: frValueDistOrNumber}>)
```

```javascript
normal(dict<{mean: frValueDistOrNumber, stdev: frValueDistOrNumber}>)
```

**Examples**

```javascript
normal(5, 1);
normal({ p5: 4, p95: 10 });
normal({ mean: 5, stdev: 2 });
```

### Lognormal Distribution

**Definitions**

```javascript
lognormal(frValueDistOrNumber, frValueDistOrNumber);
```

```javascript
lognormal(dict<{p5: frValueDistOrNumber, p95: frValueDistOrNumber}>)
```

```javascript
lognormal(dict<{mean: frValueDistOrNumber, stdev: frValueDistOrNumber}>)
```

**Examples**

```javascript
lognormal(0.5, 0.8);
lognormal({ p5: 4, p95: 10 });
lognormal({ mean: 5, stdev: 2 });
```

### Uniform Distribution

**Definitions**

```javascript
uniform(frValueDistOrNumber, frValueDistOrNumber);
```

**Examples**

```javascript
uniform(10, 12);
```

### Beta Distribution

**Definitions**

```javascript
beta(frValueDistOrNumber, frValueDistOrNumber);
```

**Examples**

```javascript
beta(20, 25);
```

### Cauchy Distribution

**Definitions**

```javascript
cauchy(frValueDistOrNumber, frValueDistOrNumber);
```

**Examples**

```javascript
cauchy(5, 1);
```

### Gamma Distribution

**Definitions**

```javascript
gamma(frValueDistOrNumber, frValueDistOrNumber);
```

**Examples**

```javascript
gamma(5, 1);
```

### Logistic Distribution

**Definitions**

```javascript
logistic(frValueDistOrNumber, frValueDistOrNumber);
```

**Examples**

```javascript
gamma(5, 1);
```

### To (Distribution)

**Definitions**

```javascript
to(frValueDistOrNumber, frValueDistOrNumber);
```

```javascript
credibleIntervalToDistribution(frValueDistOrNumber, frValueDistOrNumber);
```

**Examples**

```javascript
5 to 10
to(5,10)
-5 to 5
```

### Exponential

**Definitions**

```javascript
exponential(frValueDistOrNumber);
```

**Examples**

```javascript
exponential(2);
```

### Bernoulli

**Definitions**

```javascript
bernoulli(frValueDistOrNumber);
```

**Examples**

```javascript
bernoulli(0.5);
```

### toContinuousPointSet

Converts a set of points to a continuous distribution

**Definitions**

```javascript
toContinuousPointSet(array<dict<{x: numeric, y: numeric}>>)
```

**Examples**

```javascript
toContinuousPointSet([
  { x: 0, y: 0.1 },
  { x: 1, y: 0.2 },
  { x: 2, y: 0.15 },
  { x: 3, y: 0.1 },
]);
```

### toDiscretePointSet

Converts a set of points to a discrete distribution

**Definitions**

```javascript
toDiscretePointSet(array<dict<{x: numeric, y: numeric}>>)
```

**Examples**

```javascript
toDiscretePointSet([
  { x: 0, y: 0.1 },
  { x: 1, y: 0.2 },
  { x: 2, y: 0.15 },
  { x: 3, y: 0.1 },
]);
```

### Declaration (Continuous Function)

Adds metadata to a function of the input ranges. Works now for numeric and date inputs. This is useful when making predictions. It allows you to limit the domain that your prediction will be used and scored within.

**Definitions**

```javascript
declareFn(dict<{fn: lambda, inputs: array<dict<{min: number, max: number}>>}>)
```

**Examples**

```javascript
declareFn({
  fn: {|a,b| a },
  inputs: [
    {min: 0, max: 100},
    {min: 30, max: 50}
  ]
})
```

## Functions


### mixture

```javascript
(...distributionLike, weights:list<float>):distribution
```

**Examples**

```javascript
mixture(normal(5, 1), normal(10, 1));
```

### sample

Get one random sample from the distribution

```javascript
(distribution):number
```

**Examples**

```javascript
sample(normal(5, 2));
```

### sampleN

Get n random samples from the distribution

```javascript
(distribution, number):list<number>
```

**Examples**

```javascript
sample(normal(5, 2), 100);
```

### mean

Get the distribution mean

```javascript
(distribution):number
```

**Examples**

```javascript
mean(normal(5, 2));
```

### stdev

```javascript
(distribution):number
```

### variance

```javascript
(distribution):number
```

### mode

```javascript
(distribution):number
```

### cdf

```javascript
(distribution, number):number
```

**Examples**

```javascript
cdf(normal(5, 2), 3);
```

### pdf

```javascript
(distribution, number):number
```

**Examples**

```javascript
pdf(normal(5, 2), 3);
```

### pmf

```javascript
(distribution, number):number
```

**Examples**

```javascript
pmf(bernoulli(0.3), 0); // 0.7
```

### inv

```javascript
(distribution, number):number
```

**Examples**

```javascript
inv(normal(5, 2), 0.5);
```

### toPointSet

Converts a distribution to the pointSet format

```javascript
(distribution):pointSetDistribution
```

**Examples**

```javascript
toPointSet(normal(5, 2));
```

### toSampleSet

Converts a distribution to the sampleSet format, with n samples

```javascript
(distribution,n):sampleSetribution
```

**Examples**

```javascript
toSampleSet(normal(5, 2));
```

### truncateLeft

Truncates the left side of a distribution. Returns either a pointSet distribution or a symbolic distribution.

```javascript
(distribution, l:number, {normalize: boolean=true}):distribution
```

**Examples**

```javascript
truncateLeft(normal(5, 2), 3);
```

### truncateRight

Truncates the right side of a distribution. Returns either a pointSet distribution or a symbolic distribution.

```javascript
(distribution, r:number, {normalize: boolean=true}):distribution
```

**Examples**

```javascript
truncateLeft(normal(5, 2), 6);
```

## Scoring

### klDivergence

Kullback–Leibler divergence between two distributions

```javascript
(distribution, distribution):number
```

**Examples**

```javascript
klDivergence(normal(5, 2), normal(5, 4)); // returns 0.57
```

### logScore

```javascript
({estimate: distribution, prior?: distribution, answer: distribution|number}):number
```

**Examples**

```javascript
logScore({ estimate: normal(5, 2), prior: normal(5.5, 4), answer: 2.3 });
```

## Display

### toString

```javascript
(distribution):string
```

**Examples**

```javascript
toString(normal(5, 2));
```

### toSparkline

Produce a sparkline of length n

```javascript
(distribution, n=20):string
```

**Examples**

```javascript
toSparkline(normal(5, 2), 10);
```

### inspect

Prints the value of the distribution to the Javascript console, then returns the distribution.

```javascript
(distribution):distribution
```

**Examples**

```javascript
inspect(normal(5, 2));
```

## Normalization

### normalize

Normalize a distribution. This means scaling it appropriately so that it's cumulative sum is equal to 1.

```javascript
(distribution):distribution
```

**Examples**

```javascript
normalize(normal(5, 2));
```

### isNormalized

Check of a distribution is normalized. Most distributions are typically normalized, but there are some commands that could produce non-normalized distributions.

```javascript
(distribution):bool
```

**Examples**

```javascript
isNormalized(normal(5, 2)); // returns true
```

### integralSum

Get the sum of the integral of a distribution. If the distribution is normalized, this will be 1.

```javascript
(distribution):number
```

**Examples**

```javascript
integralSum(normal(5, 2));
```

## Algebra1

### add

```javascript
(distributionLike, distributionLike): distribution
```

### sum

```javascript
(list<distributionLike>): distribution
```

### multiply

```javascript
(distributionLike, distributionLike): distribution
```

### product

```javascript
(list<distributionLike>): distribution
```

### subtract

```javascript
(distributionLike, distributionLike): distribution
```

### divide

```javascript
(distributionLike, distributionLike): distribution
```

### pow

```javascript
(distributionLike, distributionLike): distribution
```

### exp

```javascript
(distributionLike, distributionLike): distribution
```

### log

```javascript
(distributionLike, distributionLike): distribution
```

### log10

```javascript
(distributionLike, distributionLike):distribution
```

### unaryMinus

```javascript
(distribution):distribution
```

## Algebra2

### dotAdd

```javascript
(distributionLike, distributionLike): distribution
```

### dotSum

```javascript
(list<distributionLike>): distribution
```

### dotMultiply

```javascript
(distributionLike, distributionLike): distribution
```

### dotProduct

```javascript
(list<distributionLike>): distribution
```

### dotSubtract

```javascript
(distributionLike, distributionLike): distribution
```

### dotDivide

```javascript
(distributionLike, distributionLike): distribution
```

### dotPow

```javascript
(distributionLike, distributionLike): distribution
```

### dotExp

```javascript
(distributionLike, distributionLike): distribution
```

## Algebra3

### scaleMultiply

```javascript
(distributionLike, distributionLike): distribution
```

### scalePow

```javascript
(distributionLike, distributionLike): distribution
```

### scaleExp

```javascript
(distributionLike, distributionLike): distribution
```

### scaleLog

```javascript
(distributionLike, distributionLike): distribution
```

### scaleLog10

```javascript
(distributionLike, distributionLike): distribution
```

### scaleLogWithThreshold

```javascript
(distributionLike, distributionLike, number): distribution
```
