R/SDistribution_ShiftedLoglogistic.R
ShiftedLoglogistic.RdMathematical and statistical functions for the Shifted Log-Logistic distribution, which is commonly used in survival analysis for its non-monotonic hazard as well as in economics, a generalised variant of Loglogistic.
Returns an R6 object inheriting from class SDistribution.
The Shifted Log-Logistic distribution parameterised with shape, \(\beta\), scale, \(\alpha\), and location, \(\gamma\), is defined by the pdf, $$f(x) = (\beta/\alpha)((x-\gamma)/\alpha)^{\beta-1}(1 + ((x-\gamma)/\alpha)^\beta)^{-2}$$ for \(\alpha, \beta > 0\) and \(\gamma >= 0\).
The distribution is supported on the non-negative Reals.
ShiftLLogis(scale = 1, shape = 1, location = 0)
N/A
N/A
McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.
Other continuous distributions:
Arcsine,
BetaNoncentral,
Beta,
Cauchy,
ChiSquaredNoncentral,
ChiSquared,
Dirichlet,
Erlang,
Exponential,
FDistributionNoncentral,
FDistribution,
Frechet,
Gamma,
Gompertz,
Gumbel,
InverseGamma,
Laplace,
Logistic,
Loglogistic,
Lognormal,
MultivariateNormal,
Normal,
Pareto,
Poisson,
Rayleigh,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull
Other univariate distributions:
Arcsine,
Arrdist,
Bernoulli,
BetaNoncentral,
Beta,
Binomial,
Categorical,
Cauchy,
ChiSquaredNoncentral,
ChiSquared,
Degenerate,
DiscreteUniform,
Empirical,
Erlang,
Exponential,
FDistributionNoncentral,
FDistribution,
Frechet,
Gamma,
Geometric,
Gompertz,
Gumbel,
Hypergeometric,
InverseGamma,
Laplace,
Logarithmic,
Logistic,
Loglogistic,
Lognormal,
Matdist,
NegativeBinomial,
Normal,
Pareto,
Poisson,
Rayleigh,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull,
WeightedDiscrete
distr6::Distribution -> distr6::SDistribution -> ShiftedLoglogistic
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
aliasAlias of the distribution.
packagesPackages required to be installed in order to construct the distribution.
propertiesReturns distribution properties, including skewness type and symmetry.
Inherited methods
distr6::Distribution$cdf()distr6::Distribution$confidence()distr6::Distribution$correlation()distr6::Distribution$getParameterValue()distr6::Distribution$iqr()distr6::Distribution$liesInSupport()distr6::Distribution$liesInType()distr6::Distribution$parameters()distr6::Distribution$pdf()distr6::Distribution$prec()distr6::Distribution$print()distr6::Distribution$quantile()distr6::Distribution$rand()distr6::Distribution$setParameterValue()distr6::Distribution$stdev()distr6::Distribution$strprint()distr6::Distribution$summary()distr6::Distribution$workingSupport()
new()Creates a new instance of this R6 class.
ShiftedLoglogistic$new(
scale = NULL,
shape = NULL,
location = NULL,
rate = NULL,
decorators = NULL
)scalenumeric(1))
Scale parameter of the distribution, defined on the positive Reals. scale = 1/rate.
If provided rate is ignored.
shape(numeric(1))
Shape parameter, defined on the positive Reals.
location(numeric(1))
Location parameter, defined on the Reals.
rate(numeric(1))
Rate parameter of the distribution, defined on the positive Reals.
decorators(character())
Decorators to add to the distribution during construction.
mean()The arithmetic mean of a (discrete) probability distribution X is the expectation $$E_X(X) = \sum p_X(x)*x$$ with an integration analogue for continuous distributions.
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).
median()Returns the median of the distribution. If an analytical expression is available
returns distribution median, otherwise if symmetric returns self$mean, otherwise
returns self$quantile(0.5).
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.
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.