Distributacalcul (version 0.2.2)

PGF_binom: Probability Generating Function of the Binomial distribution

Description

Probability Generating Function (PGF) of the Binomial distribution with size \(n\) and probability of success \(p\).

Usage

PGF_binom(t, size, prob)

Arguments

t

t

size

Number of trials (0 or more).

prob

Probability of success on each trial.

Value

Function :

• MGF_binom gives the moment generating function (MGF).

• E_binom gives the expected value.

• V_binom gives the variance.

• Etronq_binom gives the truncated mean.

• TVaR_binom gives the Tail Value-at-Risk.

• VaR_binom 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 \(n > 0\)

See Also

Other Binomial Distribution: E_binom(), Etronq_binom(), MGF_binom(), TVaR_binom(), V_binom(), VaR_binom()

Examples

# NOT RUN {
PGF_binom(t = 1, size = 3, prob = 0.5)

# }