# Logarithmic: Logarithmic Distribution In Distributacalcul: Probability Distribution Functions

## Description

Logarithmic distribution with probability parameter gamma.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```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. `prob` probability parameter gamma. `q` vector of quantiles. `lower.tail` logical; if TRUE (default), probabilities are P[X ≤ x], otherwise, P[X > x]. `kap` probability. `t` t.

## Details

The Logarithmic distribution with probability parameter gam has probability mass function :

-gam^k / (ln(1 - k) k)

, for k = 0, 1, 2, ..., and 0 < gam < 1].

## 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.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```dLogarithmic(x = 3, prob = 0.2) pLogarithmic(q = 3, prob = 0.2) expValLogarithmic(prob = 0.50) varLogarithmic(prob = 0.50) VatRLogarithmic(kap = 0.99, prob = 0.2) mgfLogarithmic(t = .2, prob = 0.50) pgfLogarithmic(t = .2, prob = 0.50) ```

Distributacalcul documentation built on Sept. 13, 2020, 5:19 p.m.