Distribution Creation

Normal

normal(mean: number, stdev: number)
normal({mean: number, stdev: number})
normal({p5: number, p95: number})
normal({p10: number, p90: number})
normal({p25: number, p75: number})

Creates a normal distribution with the given mean and standard deviation.

Wikipedia

Lognormal

lognormal(mu: number, sigma: number)
lognormal({mean: number, stdev: number})
lognormal({p5: number, p95: number})
lognormal({p10: number, p90: number})
lognormal({p25: number, p75: number})

Creates a lognormal distribution with the given mu and sigma.

Mu and sigma represent the mean and standard deviation of the normal which results when you take the log of our lognormal distribution. They can be difficult to directly reason about. However, there are several alternative ways to specify a lognormal distribution which are often easier to reason about.

Wikipedia

To

(5thPercentile: number) to (95thPercentile: number)
to(5thPercentile: number, 95thPercentile: number)

The to function is an easy way to generate lognormal distributions using predicted 5th and 95th percentiles. It's the same as lognormal({p5, p95}), but easier to write and read.

Arguments

• 5thPercentile: number
• 95thPercentile: number, greater than 5thPercentile

Uniform

uniform(low:number, high:number)

Creates a uniform distribution with the given low and high values.

Arguments

• low: Number
• high: Number greater than low

Point Mass

pointMass(value:number)

Creates a discrete distribution with all of its probability mass at point value.

Few Squiggle users call the function pointMass() directly. Numbers are often (but not always) converted into point mass distributions automatically, when it is appropriate.

For example, in the function mixture(1,2,normal(5,2)), the first two arguments will get converted into point mass distributions with values at 1 and 2. Therefore, this is the same as mixture(pointMass(1),pointMass(2),pointMass(5,2)).

pointMass() distributions are currently the only discrete distributions accessible in Squiggle.

Arguments

• value: Number

Beta

beta(alpha:number, beta:number)
beta({mean: number, stdev: number})

Creates a beta distribution with the given alpha and beta values. For a good summary of the beta distribution, see this explanation on Stack Overflow.

Arguments

• alpha: Number greater than zero
• beta: Number greater than zero

Mixture

mixture(...distributions: Distribution[], weights?: number[])
mixture(distributions: Distribution[], weights?: number[])
mx(...distributions: Distribution[], weights?: number[])
mx(distributions: Distribution[], weights?: number[])

The mixture mixes combines multiple distributions to create a mixture. You can optionally pass in a list of proportional weights.

Arguments

• distributions: A set of distributions or numbers, each passed as a paramater. Numbers will be converted into point mass distributions.
• weights: An optional array of numbers, each representing the weight of its corresponding distribution. The weights will be re-scaled to add to 1.0. If a weights array is provided, it must be the same length as the distribution paramaters.

Aliases

• mx

Special Use Cases of Mixtures

SampleSet.fromList

SampleSet.fromList(samples:number[])

Creates a sample set distribution using an array of samples.

Samples are converted into PDFs automatically using kernel density estimation and an approximated bandwidth. This is an approximation and can be error-prone.

Arguments

• samples: An array of at least 5 numbers.

PointSet.makeContinuous

PointSet.makeContinuous(points:{x: number, y: number})

Creates a continuous point set distribution using a list of points.

Arguments

• points: An array of at least 3 coordinates.

PointSet.makeDiscrete

PointSet.makeDiscrete(points:{x: number, y: number})

Creates a discrete point set distribution using a list of points.

Arguments

• points: An array of at least 1 coordinate.