Distributacalcul (version 0.2.2)

Etronq_binom: Truncated mean of the Binomial distribution

Description

Truncated mean of the Binomial distribution with size \(n\) and probability of success \(p\).

Usage

Etronq_binom(d, size, prob, less.than.d = TRUE)

Arguments

d

cut-off value.

size

Number of trials (0 or more).

prob

Probability of success on each trial.

less.than.d

logical; if TRUE (default) truncated mean for values <= d, otherwise, for values > d.

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(), MGF_binom(), PGF_binom(), TVaR_binom(), V_binom(), VaR_binom()

Examples

# NOT RUN {
Etronq_binom(d = 2, size = 3, prob = 0.5)
Etronq_binom(d = 0, size = 3, prob = 0.5, less.than.d = FALSE)

# }