Binomial distribution with size \(n\) and probability of success \(p\).
expValBinom(size, prob)
varBinom(size, prob)
expValTruncBinom(d, size, prob, less.than.d = TRUE)
VatRBinom(kap, size, prob)
TVatRBinom(kap, size, prob)
pgfBinom(t, size, prob)
mgfBinom(t, size, prob)Number of trials (0 or more).
Probability of success in each trial.
cut-off value.
logical; if TRUE (default) truncated mean for values <= d, otherwise, for values > d.
probability.
t.
Function :
mgfBinom gives the moment generating function (MGF).
pgfBinom gives the probability generating function (PGF).
expValBinom gives the expected value.
varBinom gives the variance.
expValTruncBinom gives the truncated mean.
TVatRBinom gives the Tail Value-at-Risk.
VatRBinom gives the Value-at-Risk.
Invalid parameter values will return an error detailing which parameter is problematic.
The binomial distribution with probability of success \(p\) for \(n\) trials has probability mass function : $$Pr(X = k) = \left(\frac{n}{k}\right) p^n (1 - p)^{n - k}$$ for \(k = 0, 1, 2, \dots, n\), \(p \in [0, 1]\), and \(n > 0\)
Function VatRBinom is a wrapper of the qbinom
function from the stats package.
expValBinom(size = 3, prob = 0.5)
#> [1] 1.5
varBinom(size = 3, prob = 0.5)
#> [1] 0.75
expValTruncBinom(d = 2, size = 3, prob = 0.5)
#> [1] 1.125
expValTruncBinom(d = 0, size = 3, prob = 0.5, less.than.d = FALSE)
#> [1] 1.5
VatRBinom(kap = 0.8, size = 5, prob = 0.2)
#> [1] 2
TVatRBinom(kap = 0.8, size = 5, prob = 0.2)
#> [1] 2.3248
pgfBinom(t = 1, size = 3, prob = 0.5)
#> [1] 1
mgfBinom(t = 1, size = 3, prob = 0.5)
#> [1] 6.425944