Statements (40)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Probability distribution
|
| gptkbp:affiliatedWith |
continuous probability distributions
|
| gptkbp:alsoKnownAs |
gptkb:lognormal_distribution
|
| gptkbp:application |
modeling income distribution
modeling stock prices modeling particle sizes modeling biological measurements |
| gptkbp:category |
distributions with positive support
right-skewed distributions |
| gptkbp:characteristic |
does not have a simple closed form
|
| gptkbp:compatibleWith |
symmetric
|
| gptkbp:cumulativeDistributionFunction |
F(x; μ, σ) = 0.5 + 0.5 erf[(ln x - μ)/(σ√2)]
|
| gptkbp:definedIn |
a probability distribution of a random variable whose logarithm is normally distributed
|
| gptkbp:describedYear |
1879
|
| gptkbp:entropy |
μ + 0.5 + ln(σ√(2π))
|
| gptkbp:firstDescribed |
gptkb:Francis_Galton
|
| gptkbp:heldBy |
positively skewed
|
| 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:momentGeneratingFunction |
does not exist for all t
|
| gptkbp:originatedIn |
multiplicative processes
|
| 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:Weibull_distribution
gptkb:Exponential_distribution gptkb:Gamma_distribution gptkb:Normal_distribution |
| gptkbp:skewness |
(exp(σ^2) + 2)√(exp(σ^2) - 1)
|
| gptkbp:supports |
x > 0
|
| gptkbp:usedIn |
biology
environmental science finance hydrology reliability engineering |
| gptkbp:variant |
[exp(σ^2) - 1] exp(2μ + σ^2)
|
| gptkbp:bfsParent |
gptkb:Log-gamma_distribution
|
| gptkbp:bfsLayer |
7
|