Logarithmic Distribution Class
Mathematical and statistical functions for the Logarithmic distribution, which is commonly used to model consumer purchase habits in economics and is derived from the Maclaurin series expansion of -ln(1-p).
The Logarithmic distribution parameterised with a parameter, θ, is defined by the pmf,
f(x) = -θ^x/xlog(1-θ)
for 0 < θ < 1.
Returns an R6 object inheriting from class SDistribution.
The distribution is supported on {1,2,3,…}.
Log(theta = 0.5)
N/A
N/A
distr6::Distribution -> distr6::SDistribution -> Logarithmic
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
packagesPackages required to be installed in order to construct the distribution.
new()
Creates a new instance of this R6 class.
Logarithmic$new(theta = NULL, decorators = NULL)
theta(numeric(1))
Theta parameter defined as a probability between 0 and 1.
decorators(character())
Decorators to add to the distribution during construction.
mean()
The arithmetic mean of a (discrete) probability distribution X is the expectation
E_X(X) = ∑ p_X(x)*x
with an integration analogue for continuous distributions.
Logarithmic$mean(...)
...Unused.
mode()
The mode of a probability distribution is the point at which the pdf is a local maximum, a distribution can be unimodal (one maximum) or multimodal (several maxima).
Logarithmic$mode(which = "all")
which(character(1) | numeric(1)
Ignored if distribution is unimodal. Otherwise "all" returns all modes, otherwise specifies
which mode to return.
variance()
The variance of a distribution is defined by the formula
var_X = E[X^2] - E[X]^2
where E_X is the expectation of distribution X. If the distribution is multivariate the covariance matrix is returned.
Logarithmic$variance(...)
...Unused.
skewness()
The skewness of a distribution is defined by the third standardised moment,
sk_X = E_X[((x - μ)/σ)^3]
where E_X is the expectation of distribution X, μ is the mean of the distribution and σ is the standard deviation of the distribution.
Logarithmic$skewness(...)
...Unused.
kurtosis()
The kurtosis of a distribution is defined by the fourth standardised moment,
k_X = E_X[((x - μ)/σ)^4]
where E_X is the expectation of distribution X, μ is the mean of the distribution and σ is the standard deviation of the distribution. Excess Kurtosis is Kurtosis - 3.
Logarithmic$kurtosis(excess = TRUE, ...)
excess(logical(1))
If TRUE (default) excess kurtosis returned.
...Unused.
mgf()
The moment generating function is defined by
mgf_X(t) = E_X[exp(xt)]
where X is the distribution and E_X is the expectation of the distribution X.
Logarithmic$mgf(t, ...)
t(integer(1))
t integer to evaluate function at.
...Unused.
cf()
The characteristic function is defined by
cf_X(t) = E_X[exp(xti)]
where X is the distribution and E_X is the expectation of the distribution X.
Logarithmic$cf(t, ...)
t(integer(1))
t integer to evaluate function at.
...Unused.
pgf()
The probability generating function is defined by
pgf_X(z) = E_X[exp(z^x)]
where X is the distribution and E_X is the expectation of the distribution X.
Logarithmic$pgf(z, ...)
z(integer(1))
z integer to evaluate probability generating function at.
...Unused.
clone()
The objects of this class are cloneable with this method.
Logarithmic$clone(deep = FALSE)
deepWhether to make a deep clone.
McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.
Other discrete distributions:
Bernoulli,
Binomial,
Categorical,
Degenerate,
DiscreteUniform,
EmpiricalMV,
Empirical,
Geometric,
Hypergeometric,
Multinomial,
NegativeBinomial,
WeightedDiscrete
Other univariate distributions:
Arcsine,
Bernoulli,
BetaNoncentral,
Beta,
Binomial,
Categorical,
Cauchy,
ChiSquaredNoncentral,
ChiSquared,
Degenerate,
DiscreteUniform,
Empirical,
Erlang,
Exponential,
FDistributionNoncentral,
FDistribution,
Frechet,
Gamma,
Geometric,
Gompertz,
Gumbel,
Hypergeometric,
InverseGamma,
Laplace,
Logistic,
Loglogistic,
Lognormal,
NegativeBinomial,
Normal,
Pareto,
Poisson,
Rayleigh,
ShiftedLoglogistic,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull,
WeightedDiscrete
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.