Distributacalcul (version 0.2.2)

PGF_logarithmic: Probability Generating Function of the Logarithmic distribution

Description

Probability Generating Function (PGF) of the Logarithmic distribution with probability parameter \(\gamma\).

Usage

PGF_logarithmic(t, prob)

Arguments

t

t.

prob

probability parameter \(\gamma\).

Value

Function :

• MGF_logarithmic gives the moment generating function (MGF).

• PGF_logarithmic gives the probability generating function (PGF).

• E_logarithmic gives the expected value.

• V_logarithmic gives the variance.

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

See Also

Other Logarithmic Distribution: E_logarithmic(), MGF_logarithmic(), V_logarithmic()

Examples

# NOT RUN {
PGF_logarithmic(t = .2, prob = 0.50)

# }