Distributions: Creation
To
(5thPercentile: number) to (95thPercentile: number)
to(5thPercentile: number, 95thPercentile: number)
The to
function is an easy way to generate simple distributions using predicted 5th and 95th percentiles.
If both values are above zero, a lognormal
distribution is used. If not, a normal
distribution is used.
- 5 to 10
- to(5,10)
- -5 to 5
- 1 to 10000
5 to 10
is entered, both numbers are positive, so it generates a lognormal distribution with 5th and 95th percentiles at 5 and 10.Arguments
5thPercentile
: number95thPercentile
: number, greater than5thPercentile
"
If you haven't tried calibration training, you're likely to be overconfident. We recommend doing calibration training to get a feel for what a 90 percent confident interval feels like.
Mixture
mixture(...distributions: Distribution[], weights?: number[])
mx(...distributions: Distribution[], weights?: number[])
mixture(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.
- Simple
- With Weights
- With Continuous and Discrete Inputs
- Array of Distributions Input
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 to1.0
. If a weights array is provided, it must be the same length as the distribution paramaters.
Aliases
mx
Special Use Cases of Mixtures
🕐 Zero or Continuous
One common reason to have mixtures of continous and discrete distributions is to handle the special case of 0. Say I want to model the time I will spend on some upcoming project. I think I have an 80% chance of doing it.
In this case, I have a 20% chance of spending 0 time with it. I might estimate my hours with,
There's a temporary bug where the below render is compressed. If you toggle the code it will fix render correctly.
🔒 Model Uncertainty Safeguarding
One technique several Foretold.io users used is to combine their main guess, with a "just-in-case distribution". This latter distribution would have very low weight, but would be very wide, just in case they were dramatically off for some weird reason.
Normal
normal(mean:number, standardDeviation:number)
Creates a normal distribution with the given mean and standard deviation.
- normal(5,1)
- normal(1G, 1G)
Arguments
mean
: Numberstandard deviation
: Number greater than zero
Log-normal
lognormal(mu: number, sigma: number)
Creates a log-normal 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.
Because of this complexity, we recommend typically using the to syntax instead of estimating mu
and sigma
directly.
Arguments
mu
: Numbersigma
: Number greater than zero
❓ Understanding mu and sigma
The log of lognormal(mu, sigma)
is a normal distribution with mean mu
and standard deviation sigma
. For example, these two distributions are identical:
Uniform
uniform(low:number, high:number)
Creates a uniform distribution with the given low and high values.
Arguments
low
: Numberhigh
: Number greater thanlow
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.
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.
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 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.
- pointMass(3)
- mixture(1,3,5)
- normal(5,2) * 6
- dotAdd(normal(5,2), 6)
- dotMultiply(normal(5,2), 6)
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.
- beta(10, 20)
- beta(1000, 1000)
- beta(1, 10)
- beta(10, 1)
- beta(0.8, 0.8)
- beta({mean: 0.39, stdev: 0.1})
Arguments
alpha
: Number greater than zerobeta
: Number greater than zero
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.
Examples
- beta(0.3, 0.3)
- beta(0.5, 0.5)
- beta(0.8, 0.8)
- beta(0.9, 0.9)
Exponential
exponential(rate:number)
Creates an exponential distribution with the given rate.
Arguments
rate
: Number greater than zero
Triangular distribution
triangular(low:number, mode:number, high:number)
Creates a triangular distribution with the given low, mode, and high values.
Arguments
low
: Numbermode
: Number greater thanlow
high
: Number greater thanmode
SampleSet.fromList
SampleSet.fromList(samples:number[])
Creates a sample set distribution using an array of samples.
Arguments
samples
: An array of at least 5 numbers.
Samples are converted into PDF shapes automatically using kernel density estimation and an approximated bandwidth. Eventually Squiggle will allow for more specificity.
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.