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Leonardo/it.grypho.scala.leonardo/it.grypho.scala.leonardo.probability

it.grypho.scala.leonardo.probability

package it.grypho.scala.leonardo.probability

Members list

Type members

Classlikes

enum DistKind

The distribution families this package knows.

The distribution families this package knows.

An enum rather than one case class per family: every family shares the same shape — a short parameter vector plus four kernels — so a single carrier keeps Session display, :save serialization and the parser to one case each instead of five.

Attributes

Companion
object
Supertypes
trait Enum
trait Serializable
trait Product
trait Equals
class Object
trait Matchable
class Any
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object DistKind

Attributes

Companion
enum
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trait Sum
trait Mirror
class Object
trait Matchable
class Any
Self type
DistKind.type
object Moments

The linearity rule table behind expect and variance.

The linearity rule table behind expect and variance.

This is the part that belongs in a computer algebra system rather than in a statistics library: E[aX + b] = a·E[X] + b is a rewrite, applied to the expression's structure before any number is computed, so it works while a and b are still free variables.

Structured exactly like scalar.Derive: a rule table, most specific first, with a give-up fallback. The give-up is None, which the calling node turns into "stay symbolic" — the termination guard every _Functional in this codebase shares.

What is deliberately not here. E[XY] = E[X]·E[Y] requires the factors to be independent, and nothing in the language expresses independence between two random variables. Asserting it would produce confidently wrong answers for correlated ones, so a product of two distinct random variables stays symbolic. A product where only one factor is random is fine, and is the a·X rule below.

Attributes

See also
Supertypes
class Object
trait Matchable
class Any
Self type
Moments.type
enum Query

What a _DistributionQuery asks of a distribution.

What a _DistributionQuery asks of a distribution.

Attributes

Companion
object
Supertypes
trait Enum
trait Serializable
trait Product
trait Equals
class Object
trait Matchable
class Any
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object Query

Attributes

Companion
enum
Supertypes
trait Sum
trait Mirror
class Object
trait Matchable
class Any
Self type
Query.type
object _Distribution

Companion for _Distribution: the validating factory.

Companion for _Distribution: the validating factory.

Attributes

Companion
class
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trait Product
trait Mirror
class Object
trait Matchable
class Any
Self type
final case class _Distribution extends _Value

A probability distribution: a concrete core._Value, bindable in an Environment and round-trippable through :save.

A probability distribution: a concrete core._Value, bindable in an Environment and round-trippable through :save.

Construction routes through _Distribution.of, which validates the parameters, so every instance that exists is a well-formed distribution.

Value parameters

kind

the family

params

the family's parameters, in the order the grammar takes them

Attributes

Companion
object
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trait Serializable
trait Product
trait Equals
trait _Value
trait _Expression
class Object
trait Matchable
class Any
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case class _DistributionOf(kind: DistKind, args: List[_Expression]) extends _Expression

Builds a distribution from parameter expressions: normal(mu, sigma) and friends.

Builds a distribution from parameter expressions: normal(mu, sigma) and friends.

The node/value split _Matrix has with _MatrixValue: this is the symbolic form, whose eval folds to a _Distribution once every parameter reduces to a number. It keeps normal(m, s) meaningful while m and s are still free variables.

Value parameters

args

the parameter expressions, in the family's declared order

kind

the family

Attributes

Supertypes
trait Serializable
trait Product
trait Equals
trait _Expression
class Object
trait Matchable
class Any
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case class _DistributionQuery(query: Query, dist: _Expression, args: List[_Expression]) extends _Expression

A numeric question about a distribution: pdf, cdf, prob or quantile.

A numeric question about a distribution: pdf, cdf, prob or quantile.

One node for all four rather than four nodes, for the same reason DistKind is one enum: they differ only in which kernel they call.

Why prob(d, lo, hi) and not P(X < 2). The grammar has no comparison operators — only = and ==, which build equations — so a predicate like X < 2 cannot be expressed. Adding < and > would be a change to the expression language, not to this domain. An interval is the honest shape available today.

Value parameters

args

the query's own arguments (one for pdf/cdf/quantile, two for prob)

dist

the distribution expression

query

the question

Attributes

Supertypes
trait Serializable
trait Product
trait Equals
trait _Expression
class Object
trait Matchable
class Any
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case class _Expectation(e: _Expression, x: Option[_Variable]) extends _Expression

The expectation expect(e, X), or expect(d) for a distribution's own mean.

The expectation expect(e, X), or expect(d) for a distribution's own mean.

Why not E[·]. Square brackets are the matrix literal, so E[X] would parse as E times a one-element matrix. expect is unambiguous and needs no grammar change.

The one-argument form is the mean of a distribution; the two-argument form is E[e] where x names the random variable inside e, and is where the linearity rules live.

Value parameters

e

the expression whose expectation is wanted, or the distribution itself

x

the random variable, or None for the one-argument form

Attributes

Supertypes
trait Serializable
trait Product
trait Equals
trait _Expression
class Object
trait Matchable
class Any
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case class _Variance(e: _Expression, x: Option[_Variable]) extends _Expression

The variance variance(e, X), or variance(d) for a distribution's own variance.

The variance variance(e, X), or variance(d) for a distribution's own variance.

Value parameters

e

the expression whose variance is wanted, or the distribution itself

x

the random variable, or None for the one-argument form

Attributes

Supertypes
trait Serializable
trait Product
trait Equals
trait _Expression
class Object
trait Matchable
class Any
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