Cumulative density function of the Loglogistic distribution

Cumulative density function of the Loglogistic distribution with shape parameter \(\tau\) and scale parameter \(\lambda\).

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

Arguments

q	quantile.
shape	shape parameter \(\tau\), must be positive integer.
rate	alternative parameterization the scale parameter, rate = 1 / scale.
scale	\(\lambda\) rate parameter, must be positive.
lower.tail	logical; if \codeTRUE (default) probabilities are Pr(M <= k), otherwise, Pr(M > k).

Value

Function :

• dllogis gives the density function.

• pllogis gives the cumulative density function.

• E_llogis gives the expected value.

• V_llogis gives the variance.

• kthmoment_llogis gives the kth moment.

• Etrunc_llogis gives the truncated mean.

• SL_llogis gives the stop-loss.

• Elim_llogis gives the limited mean.

• Mexcess_llogis gives the mean excess loss.

• TVaR_llogis gives the Tail Value-at-Risk.

• VaR_llogis gives the 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 \(x \in \mathcal{R}^+\), \(\lambda, \tau > 0\).

See also

Other Loglogistic Distribution: E_llogis(), Elim_llogis(), Etrunc_llogis(), Mexcess_llogis(), SL_llogis(), TVaR_llogis(), V_llogis(), VaR_llogis(), dllogis(), kthmoment_llogis()

Examples

# 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