ranvar

ranvar, contextual keyword

The ranvar type represents a probability distribution over integers.

r = poisson(2)

show summary "Ranvar" with
  mean(r) as "Mean"
  dispersion(r) as "Dispersion"

This outputs the following summary:

ranvar, function

def nosort process ranvar(a: number): ranvar
def nosort process ranvar(a: number, w: number): ranvar

Builds an empirical ranvar from observations a. The weighted overload uses non-negative weights w, normalized within each group.

• a: the observations (rounded to integers).
• w: the weights (non-negative; if their sum is zero, a warning is emitted).

Examples

table T = with
  [| as A, as G |]
  [| 1, "a" |]
  [| 2, "a" |]
  [| 1, "b" |]
  [| 3, "b" |]

table G[gdim] = by T.G

show table "Empirical means" with
  gdim
  mean(ranvar(T.A)) as "Mean"
  group by gdim

This outputs the following table:

table T = with
  [| as A, as W, as G |]
  [| 1, 1.0, "a" |]
  [| 2, 2.0, "a" |]
  [| 1, 0.5, "b" |]
  [| 3, 1.5, "b" |]

table G[gdim] = by T.G

show table "Weighted means" with
  gdim
  mean(ranvar(T.A, T.W)) as "Mean"
  group by gdim

This outputs the following table:

Remarks

The aggregator returns dirac(0) on empty groups and when weights sum to zero.

ranvar, montecarlo accumulator

The accumulator returns the empirical distribution of the sampled values. The target may be a scalar or a vector. In the vector case, one empirical ranvar is accumulated per line.

r = poisson(3)
montecarlo 1000 with
  dev = random.ranvar(r)
  sample r2 = ranvar(dev)

show summary "Empirical ranvar" with
  mean(r2) as "Mean"
  dispersion(r2) as "Dispersion"

This outputs the following summary:

table T = extend.range(3)

montecarlo 100 with
  sample T.R = ranvar(random.normal(T.N, 0.1))

show table "Vector empirical ranvars" with
  T.N
  mean(T.R) as "Mean"
  dispersion(T.R) as "Dispersion"