Distributacalcul (version 0.2.2)

MGF_exp: Moment Generating Function of the Exponential distribution

Description

Moment Generating Function (MGF) of the Exponential distribution with rate parameter $\beta$.

Usage

MGF_exp(t, rate = 1/scale, scale = 1/rate)

Arguments

t

t.

rate

$\beta$ is the rate parameter, must be positive.

scale

alternative parameterization to rate parameter, scale = 1 / rate.

Value

Function :

• MGF_exp gives the moment generating function (MGF).

• E_exp gives the expected value.

• V_exp gives the variance.

• kthmoment_exp gives the kth moment.

• Etronq_exp gives the truncated mean.

• SL_exp gives the stop-loss.

• Elim_exp gives the limited mean.

• Mexcess_exp gives the mean excess loss.

• TVaR_exp gives the Tail Value-at-Risk.

• VaR_exp gives the Value-at-Risk.

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

Details

The Exponential distribution with rate parameter $\beta$ has density: $$f\left(x\right)=\frac{1}{\beta }{\text{e}}^{-\beta x}$$ for $x\in {\mathcal{R}}^{+}$, $\beta >0$.

See Also

Other Exponential Distribution: E_exp(), Elim_exp(), Etronq_exp(), Mexcess_exp(), SL_exp(), TVaR_exp(), V_exp(), VaR_exp(), kthmoment_exp()

Examples

# NOT RUN {
MGF_exp(t = 1, rate = 5)

# }