Logarithmic.Rd
Logarithmic distribution with probability parameter \(\gamma\).
dLogarithmic(x, prob) pLogarithmic(q, prob, lower.tail = TRUE) expValLogarithmic(prob) varLogarithmic(prob) VatRLogarithmic(kap, prob) mgfLogarithmic(t, prob) pgfLogarithmic(t, prob)
x | vector of quantiles. |
---|---|
prob | probability parameter \(\gamma\). |
q | vector of quantiles. |
lower.tail | logical; if TRUE (default), probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\). |
kap | probability. |
t | t. |
Function :
dLogarithmic
gives the probability density function (PDF).
pLogarithmic
gives the cumulative density function (CDF).
expValLogarithmic
gives the expected value.
varLogarithmic
gives the variance.
VatRLogarithmic
gives the Value-at-Risk.
mgfLogarithmic
gives the moment generating function (MGF).
pgfLogarithmic
gives the probability generating function (MGF).
Invalid parameter values will return an error detailing which parameter is problematic.
The Logarithmic distribution with probability parameter \(\gamma\) has probability mass function : $$Pr(X = k) = \frac{-\gamma^{k}}{\ln(1 - \gamma)k}$$, for \(k = 0, 1, 2, \dots\), and \(\gamma \in (0, 1)\)].
dLogarithmic(x = 3, prob = 0.2)#> [1] 0.01195045pLogarithmic(q = 3, prob = 0.2)#> [1] 0.9978629expValLogarithmic(prob = 0.50)#> [1] 1.442695varLogarithmic(prob = 0.50)#> [1] -1.608042VatRLogarithmic(kap = 0.99, prob = 0.2)#> [1] 3mgfLogarithmic(t = .2, prob = 0.50)#> [1] 1.361051pgfLogarithmic(t = .2, prob = 0.50)#> [1] 0.1520031