Distributacalcul (version 0.4.0)

Exp: Exponential Distribution

Description

Exponential distribution with rate parameter \(\beta\).

Usage

expValExp(rate = 1/scale, scale = 1/rate)
varExp(rate = 1/scale, scale = 1/rate)
kthMomentExp(k, rate = 1/scale, scale = 1/rate)
expValLimExp(d, rate = 1/scale, scale = 1/rate)
expValTruncExp(d, rate = 1/scale, scale = 1/rate, less.than.d = TRUE)
stopLossExp(d, rate = 1/scale, scale = 1/rate)
meanExcessExp(d, rate = 1/scale, scale = 1/rate)
VatRExp(kap, rate = 1/scale, scale = 1/rate)
TVatRExp(kap, rate = 1/scale, scale = 1/rate)
mgfExp(t, rate = 1/scale, scale = 1/rate)

Value

Function :

• expValExp gives the expected value.

• varExp gives the variance.

• kthMomentExp gives the kth moment.

• expValLimExp gives the limited mean.

• expValTruncExp gives the truncated mean.

• stopLossExp gives the stop-loss.

• meanExcessExp gives the mean excess loss.

• VatRExp gives the Value-at-Risk.

• TVatRExp gives the Tail Value-at-Risk.

• mgfExp gives the moment generating function (MGF).

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

Arguments

rate

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

scale

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

k

kth-moment.

d

cut-off value.

less.than.d

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

kap

probability.

t

t.

Details

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

Examples

# With scale parameter
expValExp(scale = 4)

# With rate parameter
expValExp(rate = 0.25)

# With scale parameter
varExp(scale = 4)

# With rate parameter
varExp(rate = 0.25)

# With scale parameter
kthMomentExp(k = 2, scale = 4)

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

# With scale parameter
expValLimExp(d = 2, scale = 4)

# With rate parameter
expValLimExp(d = 2, rate = 0.25)

# With scale parameter
expValTruncExp(d = 2, scale = 4)

# With rate parameter, values greater than d
expValTruncExp(d = 2, rate = 0.25, less.than.d = FALSE)

# With scale parameter
stopLossExp(d = 2, scale = 4)

# With rate parameter
stopLossExp(d = 2, rate = 0.25)

# With scale parameter
meanExcessExp(d = 2, scale = 4)

# With rate parameter
meanExcessExp(d = 5, rate = 0.25)

# With scale parameter
VatRExp(kap = .99, scale = 4)

# With rate parameter
VatRExp(kap = .99, rate = 0.25)

# With scale parameter
TVatRExp(kap = .99, scale = 4)

# With rate parameter
TVatRExp(kap = .99, rate = 0.25)

mgfExp(t = 1, rate = 5)