Distributacalcul (version 0.2.2)

Etronq_beta: Truncated mean of the Beta distribution

Description

Truncated mean of the Beta distribution with shape parameters \(\alpha\) and \(\beta\).

Usage

Etronq_beta(d, shape1, shape2, less.than.d = TRUE)

Arguments

d

cut-off value. Recall the the domain is limited between 0 and 1.

shape1

shape parameter \(\alpha\), must be positive.

shape2

shape parameter \(\beta\), must be positive.

less.than.d

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

Value

Function :

• MGF_beta gives the moment generating function (MGF).

• E_beta gives the expected value.

• V_beta gives the variance.

• kthmoment_beta gives the kth moment.

• Etronq_beta gives the truncated mean.

• SL_beta gives the stop-loss.

• Elim_beta gives the limited mean.

• Mexcess_beta gives the mean excess loss.

• TVaR_beta gives the Tail Value-at-Risk.

Invalid parameter values will return an error detailing which parameter is problematic.

Details

The Beta distribution with shape parameters \(\alpha\) and \(\beta\) has density: $$f\left(x\right) = \frac{\Gamma(\alpha + \beta)}{\Gamma(\alpha) % \Gamma(\beta)} x^{\alpha - 1} (1 - x)^(\beta - 1)$$ for \(x \in [0, 1]\), \(\alpha, \beta > 0\).

See Also

Other Beta Distribution: E_beta(), Elim_beta(), MGF_beta(), Mexcess_beta(), SL_beta(), TVaR_beta(), V_beta(), VaR_beta(), kthmoment_beta()

Examples

# NOT RUN {
Etronq_beta(d = 0.4, shape1 = 4, shape2 = 5)
Etronq_beta(d = 0.4, shape1 = 4, shape2 = 5, less.than.d = FALSE)

# }