Distributacalcul (version 0.2.2)

kthmoment_exp: kth moment of the Exponential distribution

Description

kth moment of the Exponential distribution with rate parameter \(\beta\).

Usage

kthmoment_exp(k, rate = 1/scale, scale = 1/rate)

Arguments

k

kth-moment.

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: $$f\left(x\right) = \frac{1}{\beta}% \textrm{e}^{-\beta x}$$ for \(x \in \mathcal{R}^+\), \(\beta > 0\).

See Also

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

Examples

# NOT RUN {
# With scale parameter
kthmoment_exp(k = 2, scale = 4)

# With rate parameter
kthmoment_exp(k = 2, rate = 0.25)

# }