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Lognormal Distribution

Parameters

- continuous parameter ()
- continuous parameter
- continuous location parameter ( yields the two-parameter Lognormal distribution)

Domain

Three-Parameter Lognormal Distribution

Probability Density Function

Cumulative Distribution Function

Two-Parameter Lognormal Distribution

Probability Density Function

Cumulative Distribution Function


where is the Laplace Integral.

Worksheet and VBA Functions

The following worksheet and VBA functions are available for this distribution:

Description
VBA Functions
Worksheet Functions
Distribution Fitting - =DistFit("Lognormal";Data;[Options]1)
Probability Density Function LognormalPdf(x,sigma,mu,[gamma]) =LognormalPdf(sigma;mu;[gamma])
=DistPdf("Lognormal(sigma;mu;[gamma])";x)
Cumulative Distribution Function LognormalCdf(x,sigma,mu,[gamma]) =LognormalCdf(sigma;mu;[gamma])
=DistCdf("Lognormal(sigma;mu;[gamma])";x)
Survival Function LognormalSurv(x,sigma,mu,[gamma]) =DistSurv("Lognormal(sigma;mu;[gamma])";x)
Hazard Function LognormalHaz(x,sigma,mu,[gamma]) =LognormalHaz(sigma;mu;[gamma])
=DistHaz("Lognormal(sigma;mu;[gamma])";x)
Cumulative Hazard Function LognormalCumHaz(x,sigma,mu,[gamma]) =DistCumHaz("Lognormal(sigma;mu;[gamma])";x)
Inverse CDF (Quantile Function) LognormalInv(P,sigma,mu,[gamma]) =LognormalInv(sigma;mu;[gamma])
=DistInv("Lognormal(sigma;mu;[gamma])";P)
Random Numbers LognormalRand(sigma,mu,[gamma]) =LognormalRand(sigma;mu;[gamma])
=DistRand("Lognormal(sigma;mu;[gamma])")
Mode LognormalMode(sigma,mu,[gamma]) =DistMode("Lognormal(sigma;mu;[gamma])")
Mean LognormalMean(sigma,mu,[gamma]) =LognormalMean(sigma;mu;[gamma])
=DistMean("Lognormal(sigma;mu;[gamma])")
Variance LognormalVar(sigma,mu,[gamma]) =LognormalVar(sigma;mu;[gamma])
=DistVar("Lognormal(sigma;mu;[gamma])")
Standard Deviation LognormalStdev(sigma,mu,[gamma]) =LognormalStdev(sigma;mu;[gamma])
=DistStdev("Lognormal(sigma;mu;[gamma])")
Skewness LognormalSkew(sigma,mu,[gamma]) =DistSkew("Lognormal(sigma;mu;[gamma])")
(Excess) Kurtosis LognormalKurt(sigma,mu,[gamma]) =DistKurt("Lognormal(sigma;mu;[gamma])")

  1. The Options parameter is optional. Possible options: "gamma=value"  (example: "gamma=0")
  2. The gamma parameter is optional (the default value is 0).
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