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)vector of quantiles.
probability parameter \(\gamma\).
logical; if TRUE (default), probabilities are \(P[X \le x]\), otherwise, \(P[X > x]\).
probability.
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] 0.01195045
pLogarithmic(q = 3, prob = 0.2)
#> [1] 0.9978629
expValLogarithmic(prob = 0.50)
#> [1] 1.442695
varLogarithmic(prob = 0.50)
#> [1] -1.608042
VatRLogarithmic(kap = 0.99, prob = 0.2)
#> [1] 3
mgfLogarithmic(t = .2, prob = 0.50)
#> [1] 1.361051
pgfLogarithmic(t = .2, prob = 0.50)
#> [1] 0.1520031