Student[Statistics]
LogNormalRandomVariable
log normal random variable
Calling Sequence
Parameters
Description
Examples
References
Compatibility
LogNormalRandomVariable(mu, sigma)
mu
-
mean log parameter
sigma
scale parameter
The log normal random variable is a continuous probability random variable with probability density function given by:
ft=0t<02ⅇ−lnt−μ22σ22tσπotherwise
subject to the following conditions:
μ::real,0<σ
The LogNormal variate with mean log parameter mu and scale parameter sigma is related to the Normal variate by LogNormal(mu,sigma) ~ exp(Normal(mu,sigma)).
withStudentStatistics:
X≔LogNormalRandomVariableμ,σ:
PDFX,u
0u<02ⅇ−lnu−μ22σ22uσπotherwise
PDFX,0.5
0.7978845605ⅇ−0.5000000000−0.6931471806−1.μ2σ2σ
MeanX
ⅇμ+σ22
VarianceX
ⅇσ2+2μⅇσ2−1
Y≔LogNormalRandomVariable1,2:
PDFY,x,output=plot
CDFY,x
0x<012+erflnx−1242otherwise
CDFY,4,output=plot
Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions. 3rd ed. Hoboken: Wiley, 2000.
Johnson, Norman L.; Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.
Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.
The Student[Statistics][LogNormalRandomVariable] command was introduced in Maple 18.
For more information on Maple 18 changes, see Updates in Maple 18.
See Also
Statistics[Distributions][LogNormal]
Student
Student[Statistics][NormalRandomVariable]
Student[Statistics][RandomVariable]
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