Functions Reference
Operating on distributions
Here are the ways we combine distributions.
Addition
A horizontal right shift. The addition operation represents the distribution of the sum of the value of one random sample chosen from the first distribution and the value one random sample chosen from the second distribution.
Subtraction
A horizontal left shift. A horizontal right shift. The substraction operation represents the distribution of the value of one random sample chosen from the first distribution minus the value of one random sample chosen from the second distribution.
Multiplication
A proportional scaling. The addition operation represents the distribution of the multiplication of the value of one random sample chosen from the first distribution times the value one random sample chosen from the second distribution.
We also provide concatenation of two distributions as a syntax sugar for *
Division
A proportional scaling (normally a shrinking if the second distribution has values higher than 1). The addition operation represents the distribution of the division of the value of one random sample chosen from the first distribution over the value one random sample chosen from the second distribution. If the second distribution has some values near zero, it tends to be particularly unstable.
Exponentiation
A projection over a contracted x-axis. The exponentiation operation represents the distribution of the exponentiation of the value of one random sample chosen from the first distribution to the power of the value one random sample chosen from the second distribution.
Taking the base e exponential
Taking logarithms
A projection over a stretched x-axis.
Base x
Validity
xmust be a scalar- See the current discourse
Pointwise addition
For every point on the x-axis, operate the corresponding points in the y axis of the pdf.
Pointwise operations are done with PointSetDist internals rather than SampleSetDist internals.
TODO: this isn't in the new interpreter/parser yet.
Pointwise subtraction
TODO: this isn't in the new interpreter/parser yet.
Pointwise multiplication
Pointwise division
Pointwise exponentiation
Standard functions on distributions
Probability density function
The pdf(dist, x) function returns the density of a distribution at the
given point x.
Validity
xmust be a scalardistmust be a distribution
Cumulative density function
The cdf(dist, x) gives the cumulative probability of the distribution
or all values lower than x. It is the inverse of inv.
Validity
xmust be a scalardistmust be a distribution
Inverse CDF
The inv(dist, prob) gives the value x or which the probability for all values
lower than x is equal to prob. It is the inverse of cdf. In the literature, it
is also known as the quantiles function.
Validity
probmust be a scalar (please only put it in(0,1))distmust be a distribution
Mean
The mean(distribution) function gives the mean (expected value) of a distribution.
Sampling a distribution
The sample(distribution) samples a given distribution.
Converting between distribution formats
Recall the three formats of distributions. We can force any distribution into SampleSet format
Or PointSet format
toSampleSet has two signatures
Above, we saw the unary toSampleSet, which uses an internal hardcoded number of samples. If you'd like to provide the number of samples, it has a binary signature as well (floored)
Validity
- Second argument to
toSampleSetmust be a number.
Normalization
Some distribution operations (like horizontal shift) return an unnormalized distriibution.
We provide a normalize function
Validity - Input to normalize must be a dist
We provide a predicate isNormalized, for when we have simple control flow
Validity
- Input to
isNormalizedmust be a dist
inspect
You may like to debug by right clicking your browser and using the inspect functionality on the webpage, and viewing the console tab. Then, wrap your squiggle output with inspect to log an internal representation.
Save for a logging side effect, inspect does nothing to input and returns it.
Truncate
You can cut off from the left
You can cut off from the right
You can cut off from both sides