Statements (33)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:organization
|
| gptkbp:alsoKnownAs |
gptkb:lognormal_distribution
|
| gptkbp:application |
modeling income distribution
modeling particle size distribution modeling size of living tissue modeling stock prices |
| gptkbp:cumulativeDistributionFunction |
Φ((ln x - μ)/σ), x > 0
|
| gptkbp:definedIn |
a probability distribution of a random variable whose logarithm is normally distributed
|
| https://www.w3.org/2000/01/rdf-schema#label |
log-normal distribution
|
| 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:origin |
described by Francis Galton in 1879
|
| 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:property |
all moments exist
multiplicative product of many independent positive random variables tends to be log-normally distributed not closed under addition positively skewed |
| gptkbp:relatedTo |
gptkb:normal_distribution
gptkb:Weibull_distribution gptkb:exponential_distribution |
| gptkbp:skewness |
(exp(σ^2) + 2)√(exp(σ^2) - 1)
|
| gptkbp:supports |
(0, ∞)
|
| gptkbp:usedIn |
biology
environmental science finance reliability engineering |
| gptkbp:variant |
[exp(σ^2) - 1] exp(2μ + σ^2)
|
| gptkbp:bfsParent |
gptkb:Gaussian_distribution
|
| gptkbp:bfsLayer |
5
|