9.6 Low-Level Distribution Functions

9.6 Low-Level Distribution Functions🔗ℹ

The following functions are provided for users who need lower overhead than that of distribution objects, such as untyped Racket users (currently), and library writers who are implementing their own distribution abstractions.

Because applying these functions is meant to be fast, none of them have optional arguments. In particular, the boolean flags log? and 1-p? are always required.

Every low-level function’s argument list begins with the distribution family parameters. In the case of pdfs and cdfs, these arguments are followed by a domain value and boolean flags. In the case of inverse cdfs, they are followed by a probability argument and boolean flags. For sampling procedures, the distribution family parameters are followed by the requested number of random samples.

Generally, prob is a probability parameter, k is an integer domain value, x is a real domain value, p is the probability argument to an inverse cdf, and n is the number of random samples.

9.6.1 Integer Distribution Functions🔗ℹ

procedure
(flbernoulli-pdf prob k log?) → Flonum
  prob : Flonum
  k : Flonum
  log? : Any
procedure
(flbernoulli-cdf prob k log? 1-p?) → Flonum
  prob : Flonum
  k : Flonum
  log? : Any
  1-p? : Any
procedure
(flbernoulli-inv-cdf prob p log? 1-p?) → Flonum
  prob : Flonum
  p : Flonum
  log? : Any
  1-p? : Any
procedure
(flbernoulli-sample prob n) → FlVector
  prob : Flonum
  n : Integer

Low-level flonum functions used to implement bernoulli-dist.

procedure
(flbinomial-pdf count prob k log?) → Flonum
  count : Flonum
  prob : Flonum
  k : Flonum
  log? : Any
procedure
(flbinomial-cdf count prob k log? 1-p?) → Flonum
  count : Flonum
  prob : Flonum
  k : Flonum
  log? : Any
  1-p? : Any
procedure
(flbinomial-inv-cdf count prob p log? 1-p?) → Flonum
  count : Flonum
  prob : Flonum
  p : Flonum
  log? : Any
  1-p? : Any
procedure
(flbinomial-sample count prob n) → FlVector
  count : Flonum
  prob : Flonum
  n : Integer

Low-level flonum functions used to implement binomial-dist.

procedure
(flgeometric-pdf prob k log?) → Flonum
  prob : Flonum
  k : Flonum
  log? : Any
procedure
(flgeometric-cdf prob k log? 1-p?) → Flonum
  prob : Flonum
  k : Flonum
  log? : Any
  1-p? : Any
procedure
(flgeometric-inv-cdf prob p log? 1-p?) → Flonum
  prob : Flonum
  p : Flonum
  log? : Any
  1-p? : Any
procedure
(flgeometric-sample prob n) → FlVector
  prob : Flonum
  n : Integer

Low-level flonum functions used to implement geometric-dist.

procedure
(flpoisson-pdf mean k log?) → Flonum
  mean : Flonum
  k : Flonum
  log? : Any
procedure
(flpoisson-cdf mean k log? 1-p?) → Flonum
  mean : Flonum
  k : Flonum
  log? : Any
  1-p? : Any
procedure
(flpoisson-inv-cdf mean p log? 1-p?) → Flonum
  mean : Flonum
  p : Flonum
  log? : Any
  1-p? : Any
procedure
(flpoisson-sample mean n) → FlVector
  mean : Flonum
  n : Integer
procedure
(flpoisson-median mean) → Flonum
  mean : Flonum

Low-level flonum functions used to implement poisson-dist.

(flpoisson-median mean) runs faster than (flpoisson-inv-cdf mean 0.5 #f #f), significantly so when mean is large.

9.6.2 Real Distribution Functions🔗ℹ

procedure
(flbeta-pdf alpha beta x log?) → Flonum
  alpha : Flonum
  beta : Flonum
  x : Flonum
  log? : Any
procedure
(flbeta-cdf alpha beta x log? 1-p?) → Flonum
  alpha : Flonum
  beta : Flonum
  x : Flonum
  log? : Any
  1-p? : Any
procedure
(flbeta-inv-cdf alpha beta p log? 1-p?) → Flonum
  alpha : Flonum
  beta : Flonum
  p : Flonum
  log? : Any
  1-p? : Any
procedure
(flbeta-sample alpha beta n) → FlVector
  alpha : Flonum
  beta : Flonum
  n : Integer

Low-level flonum functions used to implement beta-dist.

procedure
(flcauchy-pdf mode scale x log?) → Flonum
  mode : Flonum
  scale : Flonum
  x : Flonum
  log? : Any
procedure
(flcauchy-cdf mode scale x log? 1-p?) → Flonum
  mode : Flonum
  scale : Flonum
  x : Flonum
  log? : Any
  1-p? : Any
procedure
(flcauchy-inv-cdf mode scale p log? 1-p?) → Flonum
  mode : Flonum
  scale : Flonum
  p : Flonum
  log? : Any
  1-p? : Any
procedure
(flcauchy-sample mode scale n) → FlVector
  mode : Flonum
  scale : Flonum
  n : Integer

Low-level flonum functions used to implement cauchy-dist.

procedure
(fldelta-pdf mean x log?) → Flonum
  mean : Flonum
  x : Flonum
  log? : Any
procedure
(fldelta-cdf mean x log? 1-p?) → Flonum
  mean : Flonum
  x : Flonum
  log? : Any
  1-p? : Any
procedure
(fldelta-inv-cdf mean p log? 1-p?) → Flonum
  mean : Flonum
  p : Flonum
  log? : Any
  1-p? : Any

Low-level flonum functions used to implement delta-dist.

To get delta-distributed random samples, use (make-flvector n mean).

procedure
(flexponential-pdf mean x log?) → Flonum
  mean : Flonum
  x : Flonum
  log? : Any
procedure
(flexponential-cdf mean x log? 1-p?) → Flonum
  mean : Flonum
  x : Flonum
  log? : Any
  1-p? : Any
procedure
(flexponential-inv-cdf mean p log? 1-p?) → Flonum
  mean : Flonum
  p : Flonum
  log? : Any
  1-p? : Any
procedure
(flexponential-sample mean n) → FlVector
  mean : Flonum
  n : Integer

Low-level flonum functions used to implement exponential-dist.

procedure
(flgamma-pdf shape scale x log?) → Flonum
  shape : Flonum
  scale : Flonum
  x : Flonum
  log? : Any
procedure
(flgamma-cdf shape scale x log? 1-p?) → Flonum
  shape : Flonum
  scale : Flonum
  x : Flonum
  log? : Any
  1-p? : Any
procedure
(flgamma-inv-cdf shape scale p log? 1-p?) → Flonum
  shape : Flonum
  scale : Flonum
  p : Flonum
  log? : Any
  1-p? : Any
procedure
(flgamma-sample shape scale n) → FlVector
  shape : Flonum
  scale : Flonum
  n : Integer

Low-level flonum functions used to implement gamma-dist.

procedure
(fllogistic-pdf mean scale x log?) → Flonum
  mean : Flonum
  scale : Flonum
  x : Flonum
  log? : Any
procedure
(fllogistic-cdf mean scale x log? 1-p?) → Flonum
  mean : Flonum
  scale : Flonum
  x : Flonum
  log? : Any
  1-p? : Any
procedure
(fllogistic-inv-cdf mean scale p log? 1-p?) → Flonum
  mean : Flonum
  scale : Flonum
  p : Flonum
  log? : Any
  1-p? : Any
procedure
(fllogistic-sample mean scale n) → FlVector
  mean : Flonum
  scale : Flonum
  n : Integer

Low-level flonum functions used to implement logistic-dist.

procedure
(flnormal-pdf mean stddev x log?) → Flonum
  mean : Flonum
  stddev : Flonum
  x : Flonum
  log? : Any
procedure
(flnormal-cdf mean stddev x log? 1-p?) → Flonum
  mean : Flonum
  stddev : Flonum
  x : Flonum
  log? : Any
  1-p? : Any
procedure
(flnormal-inv-cdf mean stddev p log? 1-p?) → Flonum
  mean : Flonum
  stddev : Flonum
  p : Flonum
  log? : Any
  1-p? : Any
procedure
(flnormal-sample mean stddev n) → FlVector
  mean : Flonum
  stddev : Flonum
  n : Integer

Low-level flonum functions used to implement normal-dist.

procedure
(fltriangle-pdf min max mode x log?) → Flonum
  min : Flonum
  max : Flonum
  mode : Flonum
  x : Flonum
  log? : Any
procedure
(fltriangle-cdf min max mode x log? 1-p?) → Flonum
  min : Flonum
  max : Flonum
  mode : Flonum
  x : Flonum
  log? : Any
  1-p? : Any
procedure
(fltriangle-inv-cdf min max mode p log? 1-p?) → Flonum
  min : Flonum
  max : Flonum
  mode : Flonum
  p : Flonum
  log? : Any
  1-p? : Any
procedure
(fltriangle-sample min max mode n) → FlVector
  min : Flonum
  max : Flonum
  mode : Flonum
  n : Integer

Low-level flonum functions used to implement triangle-dist.

procedure
(fluniform-pdf min max x log?) → Flonum
  min : Flonum
  max : Flonum
  x : Flonum
  log? : Any
procedure
(fluniform-cdf min max x log? 1-p?) → Flonum
  min : Flonum
  max : Flonum
  x : Flonum
  log? : Any
  1-p? : Any
procedure
(fluniform-inv-cdf min max p log? 1-p?) → Flonum
  min : Flonum
  max : Flonum
  p : Flonum
  log? : Any
  1-p? : Any
procedure
(fluniform-sample min max n) → FlVector
  min : Flonum
  max : Flonum
  n : Integer

Low-level flonum functions used to implement uniform-dist.

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

9.1	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

9.6.1	Integer Distribution Functions
9.6.2	Real Distribution Functions