mixture

mixture(T.R : ranvar) 🡒 ranvar, aggregator

Returns the mixture of ranvars. Let $X_i$ be the list of the $N$ ranvars to be aggregated, the mixture is defined by:

$$P[X = x] = \frac{1}{N} \sum_{i=1}^N P[X_i = x] $$

Example:

table T = with
  [| as A, as B |]
  [| 0,   "a"   |]
  [| 0.5, "a"   |]
  [| 0.5, "b"   |]
  [| 1,   "b"   |]
  [| 1,   "c"   |]

T.R = poisson(T.A)

table G[gdim] = by T.B

where T.B != "c"
  show table "" a1b4 with
    gdim
    mixture(T.R)
    group by gdim

On empty groups, the ranvar dirac(0) is returned.

mixture(T.r : ranvar, T.w : number) 🡒 ranvar, aggregator

todoReturns the mixture of ranvars. Let $X_i$ be the list of the $N$ ranvars to be aggregated, and $w_i$ their nonnegative weights, the mixture is defined by:

$$P[X = x] = \frac{1}{\sum_i w_i} \sum_{i=1}^N w_i P[X_i = x] $$

Example:

table T = with
  [| as A, as B, as W |]
  [| 0,   "a", 0.5 |]
  [| 0.5, "a", 0.5 |]
  [| 0.5, "b", 0.3 |]
  [| 1,   "b", 0.3 |]
  [| 1,   "c", 1.0 |]

T.R = poisson(T.A)

table G[gdim] = by T.B

where T.B != "c"
  show table "" a1b4 with
    gdim
    mixture(T.R, T.W)
    group by gdim

All weights are expected to be nonnegative, the execution will fail.

On empty groups, or on groups where the weight sum is zero, the ranvar dirac(0) is returned.

mixture(r1 : ranvar, p1 : number, r2 : ranvar) 🡒 ranvar, pure function

Same as the mixture(ranvar, number) aggregator, with:

Example:

r1 = poisson(2)
r2 = poisson(3)
show scalar "" a1b2 with mixture(r1, 0.2, r2)

mixture(r1 : ranvar, p1 : number, r2 : ranvar, p2 : number, r3 : ranvar) 🡒 ranvar, pure function

Same as the mixture(ranvar, number) aggregator, with:

Example:

r1 = poisson(2)
r2 = poisson(3)
r3 = poisson(4)
show scalar "" a1b2 with mixture(r1, 0.2, r2, 0.1, r3)

mixture(r1 : ranvar, p1 : number, r2 : ranvar, p2 : number, r3 : ranvar, p3 : number, r4 : ranvar) 🡒 ranvar, pure function

Same as the mixture(ranvar, number) aggregator, with:

Example:

r1 = poisson(2)
r2 = poisson(3)
r3 = poisson(4)
r4 = poisson(5)
show scalar "" a1b2 with mixture(r1, 0.2, r2, 0.1, r3, 0.1, r4)