|
gptkbp:instanceOf
|
gptkb:organization
|
|
gptkbp:alsoKnownAs
|
gptkb:log-normal_distribution
|
|
gptkbp:continuity
|
true
|
|
gptkbp:cumulativeDistributionFunction
|
Φ((ln x - μ)/σ), x > 0
|
|
gptkbp:definedIn
|
a probability distribution of a random variable whose logarithm is normally distributed
|
|
gptkbp:entropy
|
μ + 0.5 + ln(σ√(2π))
|
|
gptkbp:familyMember
|
gptkb:exponential_family
gptkb:location-scale_family
|
|
gptkbp:generalizes
|
normal distribution (under log transformation)
|
|
gptkbp:hasSpecialCase
|
gptkb:generalized_lognormal_distribution
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
lognormal distribution
|
|
gptkbp:introducedIn
|
1879
|
|
gptkbp:isRightSkewed
|
true
|
|
gptkbp:isUnimodal
|
true
|
|
gptkbp:kurtosis
|
exp(4σ^2) + 2exp(3σ^2) + 3exp(2σ^2) - 6
|
|
gptkbp:meaning
|
exp(μ + σ^2/2)
|
|
gptkbp:medium
|
exp(μ)
|
|
gptkbp:mode
|
exp(μ - σ^2)
|
|
gptkbp:namedFor
|
gptkb:Thorvald_N._Thiele
|
|
gptkbp:parameter
|
μ (mean of log)
σ (standard deviation of log)
|
|
gptkbp:probabilityDensityFunction
|
f(x; μ, σ) = (1/(xσ√(2π))) exp(-(ln x - μ)^2/(2σ^2)), x > 0
|
|
gptkbp:relatedTo
|
gptkb:normal_distribution
|
|
gptkbp:skewness
|
(exp(σ^2) + 2)√(exp(σ^2) - 1)
|
|
gptkbp:supports
|
(0, ∞)
|
|
gptkbp:usedFor
|
modeling income distribution
modeling stock prices
modeling particle sizes
|
|
gptkbp:usedIn
|
biology
environmental science
finance
reliability engineering
|
|
gptkbp:variant
|
[exp(σ^2) - 1] exp(2μ + σ^2)
|
|
gptkbp:bfsParent
|
gptkb:log-normal_distribution
gptkb:Johnson_distribution
|
|
gptkbp:bfsLayer
|
6
|