Discrete Probability Distributions

NoisyOr(s, leak, c1, p1, cn, pn)

Description: This function represents a noisy OR in which the effect of the parents (the causes ci) on the symptom s can be inhibited. pi represents the probability that the cause i acts on the symptom (the inhibition probability is then 1 - pi). It is also possible to define a leak probability for the set of causes that are not directly modeled.
Number of parameters: even, and >= 4
Parameter type: boolean, numerical, boolean, numerical, …, boolean, numerical
Result type: real

The conditional probability table below corresponds to NoisyOr(?N3?, 0.1, ?N1?, 0.8, ?N2?, 0.6):

N1	N2	N3 = False	N3 = True
False	False	`(1 - 0.1)`	`0.1`
False	True	`(1 - 0.1) * (1 - 0.6)`	`0.64`
True	False	`(1 - 0.1) * (1 - 0.8)`	`0.82`
True	True	`(1 - 0.1) * (1 - 0.8) * (1 - 0.6)`	`0.928`

Description: This function represents a noisy AND, i.e., the noisy OR negation.
Number of parameters: even, and >= 4
Parameter type: boolean, numerical, boolean, numerical, …, boolean, numerical
Result type: real

The conditional probability table below corresponds to NoisyAnd(?N3?, 0.1, ?N1?, 0.8, ?N2?, 0.6):

N1	N2	N3 = False	N3 = True
False	False	`0.928`	`(1 - 0.1) * (1 - 0.6) * (1 - 0.8)`
False	True	`0.82`	`(1 - 0.1) * (1 - 0.8)`
True	False	`0.64`	`(1 - 0.1) * (1 - 0.6)`
True	True	`0.1`	`(1 - 0.1)`

Description: Probability of obtaining exactly k occurrences of the same event of probability p among n independent experiments.
Number of parameters: 3
Parameter type: integer, integer, numerical
Result type: real

The probability distribution below corresponds to Binomial(?N1?, 20, 0.3):

Description: Probability of requiring k trials to have n successes of the same event of probability p among independent experiments.
Number of parameters: 3
Parameter type: integer, integer, numerical
Result type: real

The probability distribution below corresponds to NegBinomial(?N1?, 4, 0.3):

Description: Probability of requiring k independent experiments to obtain a first observation of an event of probability p.
Number of parameters: 2
Parameter type: integer, numerical
Result type: real

The probability distribution below corresponds to Geometric(?N1?, 0.3):

Description: Probability of obtaining k winning objects when choosing n objects among N, where m are winning objects.
Number of parameters: 4
Parameter type: integer, integer, integer, integer
Result type: real

The probability distribution below corresponds to Hypergeometric(?N1?, 5, 5, 20):

Description: Probability of obtaining k observations of an event in a large number of independent experiments when the mean is l.
Number of parameters: 2
Parameter type: integer, real
Result type: real

The probability distribution below corresponds to Poisson(?N1?, 18.5):