Distribution Functions
Various functions for operating on distributions
Standard Operations
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. The subtraction 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 multiplication 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 division 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.
The base e
exponential
Logarithms
A projection over a stretched x-axis.
Base x
Pointwise Operations
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.
Pointwise multiplication
Standard Functions
Probability density function
The pdf(dist, x)
function returns the density of a distribution at the
given point x.
Validity
x
must be a scalardist
must 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 quantile
.
Validity
x
must be a scalardist
must be a distribution
Quantile
The quantile(dist, prob)
gives the value x for which the sum of 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. In the optional summary statistics
panel which appears
beneath distributions, the numbers beneath 5%, 10%, 25% etc are the quantiles of that distribution
for those precentage values.
Validity
prob
must be a scalar (please only put it in(0,1)
)dist
must 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
We can convert any distribution into the SampleSet
format
Or the PointSet
format
Validity
- Second argument to
SampleSet.fromDist
must 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
isNormalized
must 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
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