binom: Binomial Distribution

In Distributacalcul: Probability Distribution Functions

Binomial Distribution

Description

Binomial distribution with size n and probability of success p.

Usage

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).
prob	Probability of success in each trial.
d	cut-off value.
less.than.d	logical; if TRUE (default) truncated mean for values <= d, otherwise, for values > d.
kap	probability.
t	t.

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

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.

Note

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

Examples

expValBinom(size = 3, prob = 0.5)

varBinom(size = 3, prob = 0.5)


expValTruncBinom(d = 2, size = 3, prob = 0.5)
expValTruncBinom(d = 0, size = 3, prob = 0.5, less.than.d = FALSE)


VatRBinom(kap = 0.8, size = 5, prob = 0.2)

TVatRBinom(kap = 0.8, size = 5, prob = 0.2)


pgfBinom(t = 1, size = 3, prob = 0.5)

mgfBinom(t = 1, size = 3, prob = 0.5)

Distributacalcul documentation built on May 29, 2024, 9:25 a.m.