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)

# }