erlang: Erlang Distribution

In Distributacalcul: Probability Distribution Functions

Description

Erlang distribution with shape parameter n and rate parameter beta.

Usage

dErlang(x, shape, rate = 1/scale, scale = 1/rate)

pErlang(q, shape, rate = 1/scale, scale = 1/rate, lower.tail = TRUE)

expValErlang(shape, rate = 1/scale, scale = 1/rate)

varErlang(shape, rate = 1/scale, scale = 1/rate)

kthMomentErlang(k, shape, rate = 1/scale, scale = 1/rate)

expValLimErlang(d, shape, rate = 1/scale, scale = 1/rate)

expValTruncErlang(d, shape, rate = 1/scale, scale = 1/rate, less.than.d = TRUE)

stopLossErlang(d, shape, rate = 1/scale, scale = 1/rate)

meanExcessErlang(d, shape, rate = 1/scale, scale = 1/rate)

VatRErlang(kap, shape, rate = 1/scale, scale = 1/rate)

TVatRErlang(kap, shape, rate = 1/scale, scale = 1/rate)

mgfErlang(t, shape, rate = 1/scale, scale = 1/rate)

Arguments

x	vector of quantiles.
shape	shape parameter n, must be a positive integer.
rate	rate parameter beta, must be positive.
scale	alternative parameterization to the rate parameter, scale = 1 / rate.
q	vector of quantiles.
lower.tail	logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x].
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 Erlang distribution with shape parameter n and rate parameter b has density:

f(x) = b^n / Γ(n) x^{n - 1} e^{-b x}

for x > 0, b > 0, n = 1, 2, 3, ....

Value

Function :

• dErlang gives the probability density function (PDF).

• pErlang gives the cumulative density function (CDF).

• expValErlang gives the expected value.

• varErlang gives the variance.

• kthMomentErlang gives the kth moment.

• expValLimErlang gives the limited mean.

• expValTruncErlang gives the truncated mean.

• stopLossErlang gives the stop-loss.

• meanExcessErlang gives the mean excess loss.

• VatRErlang gives the Value-at-Risk.

• TVatRErlang gives the Tail Value-at-Risk.

• mgfErlang gives the moment generating function (MGF).

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

Note

Function VatRErlang is a wrapper of the qgamma function from the stats package.

Examples

dErlang(x = 2, shape = 2, scale = 4)

pErlang(q = 2, shape = 2, scale = 4)

expValErlang(shape = 2, scale = 4)

varErlang(shape = 2, scale = 4)

kthMomentErlang(k = 3, shape = 2, scale = 4)

expValLimErlang(d = 2, shape = 2, scale = 4)

# With rate parameter
expValTruncErlang(d = 2, shape = 2, scale = 4)

# Values greater than d
expValTruncErlang(d = 2, shape = 2, scale = 4, less.than.d = FALSE)

stopLossErlang(d = 2, shape = 2, scale = 4)

meanExcessErlang(d = 3, shape = 2, scale = 4)

# With scale parameter
VatRErlang(kap = .2, shape = 2, scale = 4)

# With rate parameter
VatRErlang(kap = .2, shape = 2, rate = 0.25)

# With scale parameter
TVatRErlang(kap = .2, shape = 3, scale = 4)

# With rate parameter
TVatRErlang(kap = .2, shape = 3, rate = 0.25)

mgfErlang(t = 2, shape = 2, scale = .25)

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