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
Characteristic function (probability theory) Beta-binomial distribution Boltzmann distribution Uniform distribution (discrete) Geometric distribution Zeta distribution Triangular distribution Beta prime distribution Bose–Einstein statistics Erlang distribution F-distribution Fermi–Dirac statistics Generalized extreme value distribution Hotelling's T-squared distribution Rayleigh distribution Weibull distribution Cauchy distribution Gumbel distribution Stable distribution Logistic distribution Multinomial distribution Dirichlet distribution Multivariate normal distribution Wishart distribution
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