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)

## Arguments

x vector of quantiles. probability parameter $$\gamma$$. vector of quantiles. logical; if TRUE (default), probabilities are $$P[X \le x]$$, otherwise, $$P[X > x]$$. probability. t.

## Value

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.

## Details

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 $$\gamma \in (0, 1)$$].

## Examples

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