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Statistics[Distributions]

  

LogNormal

  

log normal distribution

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

LogNormal(mu, sigma)

LogNormalDistribution(mu, sigma)

Parameters

mu

-

mean log parameter

sigma

-

scale parameter

Description

• 

The log normal distribution is a continuous probability distribution with probability density function given by:

ft=0t<02&ExponentialE;lntμ22σ22tσπotherwise

  

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)).

• 

Note that the LogNormal command is inert and should be used in combination with the RandomVariable command.

Examples

withStatistics&colon;

XRandomVariableLogNormal&mu;&comma;&sigma;&colon;

PDFX&comma;u

&lcub;0u<0122&ExponentialE;12lnu&mu;2&sigma;2u&sigma;&pi;otherwise

(1)

PDFX&comma;0.5

0.7978845605&ExponentialE;0.50000000000.69314718061.&mu;2&sigma;2&sigma;

(2)

MeanX

&ExponentialE;&mu;&plus;12&sigma;2

(3)

VarianceX

&ExponentialE;&sigma;2&plus;2&mu;&ExponentialE;&sigma;21

(4)

References

  

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.

See Also

Statistics

Statistics[Distributions]

Statistics[RandomVariable]

 


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