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)

## Arguments

size 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.

## Value

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.

## Details

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 $$n > 0$$

## Note

Function VatRBinom is a wrapper of the qbinom function from the stats package.

## Examples

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] 1.125expValTruncBinom(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