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Lognormal Distribution

Parameters

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

Two-Parameter Lognormal Distribution

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).