# Logarithmic distribution

The logarithmic distribution is a discrete probability distribution and comes from the field of actuarial science. It is interesting as the amount of loss distribution, but is hardly used to determine the damage numbers.

## Definition

A discrete random variable satisfies the logarithmic distribution with parameters (number of trials ) and ( probability of success ) when the probability

Possesses.

## Properties

### Expected value

The logarithmic distribution has an expected value of

### Variance

The variance is determined to

### Coefficient of variation

From the expected value and variance are obtained immediately the coefficient of variation

### Skew

The skewness is given by:

### Characteristic function

The characteristic feature is in the form

### Generating function

For the generating function is obtained.

### Moment generating function

The moment generating function of the logarithmic distribution is

Discrete univariate distributions for finite sets: Benford | Bernoulli | beta - binomial | binomial | categorical | hypergeometric | Rademacher | generalized binomial | Zipf | Zipf - Mandelbrot

Discrete univariate distributions for infinite sets: Boltzmann | Conway - Maxwell - Poisson | negative binomial | extended negative binomial | Compound Poisson | discrete uniform | discrete phase -type | Gauss - Kuzmin | geometric | logarithmic | parabolic fractal | Poisson | Poisson - Gamma | Skellam | Yule- Simon | Zeta

Continuous univariate distributions with compact interval: Beta | Cantor | Kumaraswamy | raised cosine | Triangle | U - square | steady uniform | Wigner semicircle

Continuous univariate distributions with half-open interval: Beta prime | Bose -Einstein | Burr | Chi-Square | Coxian | Erlang | Exponential | F | Fermi -Dirac | Folded normal | Fréchet | Gamma | Gamma Gamma | extreme | generalized inverse Gaussian | semi logistically | semi- normal | Hotelling's T-square | hyper- exponential | hypoexponential | inverse chi-square | scale - inverse- chi-square | inverse Normal | inverse gamma | Levy | log-normal | log- logistically | Maxwell -Boltzmann | Maxwell speed | Nakagami | not centered chi-square | Pareto | Phase -Type | Rayleigh | relativistic Breit-Wigner | Rice | Rosin -Rammler | shifted Gompertz | truncated normal | Type -2 Gumbel | Weibull | Wilks ' lambda

Continuous univariate distributions with unbounded interval: Cauchy | extreme | exponentially Power | Fishers z | Fisher - Tippett ( Gumbel ) | generalized hyperbolic | Hyperbolic- secant | Landau | Laplace | alpha- stable | logistics | normal ( Gaussian ) | normal - inverse Gauß'sch | skew - normal | Student's t | Type -1 Gumbel | Variance gamma | Voigt

Discrete multivariate distributions: Ewen | multinomial | Dirichlet compound multinomial

Continuous multivariate distributions: Dirichlet | generalized Dirichlet | multivariate normal | multivariate Student | normal scaled inverse gamma | Normal - Gamma

Multivariate matrix distributions: Inverse Wishart | matrix normal | Wishart

- Probability distribution