NBinom {Distributacalcul} | R Documentation |
Negative Binomial Distribution
Description
Negative binomial distribution with parameters (number of successful
trials) and
(probability of success).
Usage
expValNBinom(
size,
prob = (1/(1 + beta)),
beta = ((1 - prob)/prob),
nb_tries = FALSE
)
varNBinom(
size,
prob = (1/(1 + beta)),
beta = ((1 - prob)/prob),
nb_tries = FALSE
)
mgfNBinom(
t,
size,
prob = (1/(1 + beta)),
beta = ((1 - prob)/prob),
nb_tries = FALSE
)
pgfNBinom(
t,
size,
prob = (1/(1 + beta)),
beta = ((1 - prob)/prob),
nb_tries = FALSE
)
Arguments
size |
Number of successful trials. |
prob |
Probability of success in each trial. |
beta |
Alternative parameterization of the negative binomial distribution where beta = (1 - p) / p. |
nb_tries |
logical; if |
t |
t. |
Details
When is the number of failures until the
th success,
with a probability
of a success, the negative binomial has density:
for
When is the number of trials until the
th success,
with a probability
of a success, the negative binomial has density:
for
The alternative parameterization of the negative binomial with parameter
, and
being the number of trials, has density:
for
Value
Function :
-
expValNBinom
gives the expected value. -
varNBinom
gives the variance. -
mgfNBinom
gives the moment generating function (MGF). -
pgfNBinom
gives the probability generating function (PGF).
Invalid parameter values will return an error detailing which parameter is problematic.
Examples
# Where k is the number of trials for a rth success
expValNBinom(size = 2, prob = .4)
# Where k is the number of failures before a rth success
expValNBinom(size = 2, prob = .4, nb_tries = TRUE)
# With alternative parameterization where k is the number of trials
expValNBinom(size = 2, beta = 1.5)
# Where k is the number of trials for a rth success
varNBinom(size = 2, prob = .4)
# Where k is the number of failures before a rth success
varNBinom(size = 2, prob = .4, nb_tries = TRUE)
# With alternative parameterization where k is the number of trials
varNBinom(size = 2, beta = 1.5)
mgfNBinom(t = 1, size = 4, prob = 0.5)
pgfNBinom(t = 5, size = 3, prob = 0.3)