Exp: Exponential Distribution In Distributacalcul: Probability Distribution Functions

Description

Exponential distribution with rate parameter beta.

Usage

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 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) 

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 b has density:

f≤ft(x\right) = \frac{1}{β}\textrm{e}^{-β x}

f(x) = b^a e^-b x for x > 0, b > 0.

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.

Note

Function VatRExp is a wrapper of the qexp function from the stats package.

Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 # 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) 

Distributacalcul documentation built on Sept. 13, 2020, 5:19 p.m.