llogis.Rd
Loglogistic distribution with shape parameter \(\tau\) and scale parameter \(\lambda\).
dLlogis(x, shape, rate = 1/scale, scale = 1/rate) pLlogis(q, shape, rate = 1/scale, scale = 1/rate, lower.tail = TRUE) expValLlogis(shape, rate = 1/scale, scale = 1/rate) varLlogis(shape, rate = 1/scale, scale = 1/rate) kthMomentLlogis(k, shape, rate = 1/scale, scale = 1/rate) expValLimLlogis(d, shape, rate = 1/scale, scale = 1/rate) expValTruncLlogis(d, shape, rate = 1/scale, scale = 1/rate, less.than.d = TRUE) stopLossLlogis(d, shape, rate = 1/scale, scale = 1/rate) meanExcessLlogis(d, shape, rate = 1/scale, scale = 1/rate) VatRLlogis(kap, shape, rate = 1/scale, scale = 1/rate) TVatRLlogis(kap, shape, rate = 1/scale, scale = 1/rate)
x | vector of quantiles. |
---|---|
shape | shape parameter \(\tau\), must be positive |
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 \(P[X \le x]\), otherwise, \(P[X > x]\). |
k | kth-moment. |
d | cut-off value. |
less.than.d | logical; if |
kap | probability. |
Function :
dLlogis
gives the probability density function (PDF).
pLlogis
gives the cumulative density function (CDF).
expValLlogis
gives the expected value.
varLlogis
gives the variance.
kthMomentLlogis
gives the kth moment.
expValLimLlogis
gives the limited mean.
expValTruncLlogis
gives the truncated mean.
stopLossLlogis
gives the stop-loss.
meanExcessLlogis
gives the mean excess loss.
VatRLlogis
gives the Value-at-Risk.
TVatRLlogis
gives the Tail Value-at-Risk.
Invalid parameter values will return an error detailing which parameter is problematic.
The loglogistic distribution with shape parameter \(\tau\) and scale parameter \(\lambda\) has density: $$\frac{\tau \lambda^\tau x^{\tau -1}}{(\lambda^{\tau }+x^{\tau })^{2}}$$ for \(x \in \mathcal{R}^+\), \(\lambda, \tau > 0\).
dLlogis(x = 2, shape = 2, scale = 4)#> [1] 0.01514793# With scale parameter pLlogis(q = 3, shape = 3, scale = 5)#> [1] 0.9997038# With rate parameter pLlogis(q = 3, shape = 3, rate = 0.2)#> [1] 0.9997038# Survival function pLlogis(q = 3, shape = 3, rate = 0.2, lower.tail = FALSE)#> [1] 0.0002962085expValLlogis(shape = 2, scale = 4)#> [1] 6.283185varLlogis(shape = 3, scale = 4)#> [1] 15.29977kthMomentLlogis(k = 3, shape = 5, scale = 4)#> [1] 126.8454expValLimLlogis(d = 2, shape = 2, scale = 4)#> [1] 1.85459# With rate parameter expValTruncLlogis(d = 2, shape = 2, scale = 4)#> [1] 0.2545904# Values greater than d expValTruncLlogis(d = 2, shape = 2, scale = 4, less.than.d = FALSE)#> [1] 6.028595stopLossLlogis(d = 2, shape = 2, scale = 4)#> [1] 4.428595meanExcessLlogis(d = 3, shape = 2, scale = 4)#> [1] 5.795595# With scale parameter VatRLlogis(kap = .2, shape = 2, scale = 4)#> [1] 2# With rate parameter VatRLlogis(kap = .2, shape = 2, rate = 0.25)#> [1] 2# With scale parameter TVatRLlogis(kap = .2, shape = 3, scale = 4)#> [1] 5.588911# With rate parameter TVatRLlogis(kap = .2, shape = 3, rate = 0.25)#> [1] 5.588911