9.3 Finite Distribution Families

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1 | Constants and Elementary Functions
2 | Flonums
3 | Special Functions
4 | Number Theory
5 | Arbitrary-Precision Floating-Point Numbers (Bigfloats)
6 | Arrays
7 | Matrices and Linear Algebra
8 | Statistics Functions
9 | Probability Distributions
10 | Stuff That Doesn’t Belong Anywhere Else

▼ | 9 | Probability Distributions

9.1 | Distribution Objects
9.2 | Distribution Types and Operations
9.3 | Finite Distribution Families
9.4 | Integer Distribution Families
9.5 | Real Distribution Families
9.6 | Low-Level Distribution Functions

► | 9.3 | Finite Distribution Families

9.3.1 | Unordered Discrete Distributions

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9.3.1`` Unordered Discrete Distributions
Discrete-Dist
discrete-dist
discrete-dist-values
discrete-dist-probs

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#### 9.3`` Finite Distribution Families

##### 9.3.1`` Unordered Discrete Distributions

> syntax (Discrete-Dist A)
> procedure (discrete-dist xs) → (Discrete-Dist A)
> xs : (Sequenceof A)
> (discrete-dist xs ws) → (Discrete-Dist A)
> xs : (Sequenceof A)
> ws : (Sequenceof Real)
> procedure (discrete-dist-values d) → (Listof A)
> d : (Discrete-Dist A)
> procedure (discrete-dist-probs d) → (Listof Positive-Flonum)
> d : (Discrete-Dist A)

Represents families of unordered, discrete distributions over values of type A, with equality decided by equal?.

The weights in ws must be nonnegative, and are treated as unnormalized probabilities. When ws is not given, the values in xs are assigned uniform probabilities.

The type (Discrete-Dist A) is a subtype of (dist A A). This means that discrete distribution objects are unordered, and thus have only a pdf and a procedure to generate random samples.

Note, however, that the discrete-dist-values and discrete-dist-probs functions produce lists that may be paired; that is, if the result of calling discrete-dist-values on a given distribution produces a list whose third element is 'a, and the result of calling discrete-dist-probs on the same distribution produces a list whose third element is 0.25, then the given distribution associates the probability 0.25 with the value 'a.

Examples:

> > (define xs '(a b c))
> > (define d (discrete-dist xs '(2 5 3)))
> > (define n 500)
> > (define h (samples->hash (sample d n)))
> > (plot (list (discrete-histogram
> (map vector xs (map (distribution-pdf d) xs))
> #:x-min 0 #:skip 2 #:label "P[x]")
> (discrete-histogram
> (map vector xs (map (λ (x) (/ (hash-ref h x) n)) xs))
> #:x-min 1 #:skip 2 #:line-style 'dot #:alpha 0.5
> #:label "est. P[x]")))

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