Loglogistic Distribution — llogis • Distributacalcul

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)

Arguments

x, q: 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.
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 TRUE (default) truncated mean for values <= d, otherwise, for values > d.
kap: probability.

Value

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.

Details

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 $x \in \mathcal{R}^+$, $\lambda, \tau > 0$.

Examples

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] 0.0002962085

expValLlogis(shape = 2, scale = 4)
#> [1] 6.283185

varLlogis(shape = 3, scale = 4)
#> [1] 15.29977

kthMomentLlogis(k = 3, shape = 5, scale = 4)
#> [1] 126.8454

expValLimLlogis(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] 6.028595

stopLossLlogis(d = 2, shape = 2, scale = 4)
#> [1] 4.428595

meanExcessLlogis(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