Lognormal distribution in base B






Format: LognormalB(m, s, B,)

 

The definition of a Lognormally distributed random variable is that the log of that variable is Normally distributed. Thus, an alternative way of defining a Lognormally distributed variable is to specify the mean and standard deviation of the corresponding Normal distribution. One usually defines the Lognormal distribution in terms of its mean and standard deviation, as in the Lognormal distribution. However, the LognormalB distribution uses any value B as the base:

B^Normal(m,s) = LognormalB(m,s,B)

Uses

Taking logs might seem like an unnecessary complication, but many people whose work involves statistics and who consider Lognormal random variables, habitually record and discuss the mean and the standard deviation of the corresponding Normal distribution, for example in experiments involving the growth of bacteria. They do this because variables like the number of bacteria, or the impact of a natural disaster, can have wildly varying means and standard deviations between experiments, and taking logs can make comparisons much easier. Most people would usually use 10 as the base value B.

Alternative parametrizations

The Lognormal distribution has as its parameters the mean and standard deviation of the distribution itself.

The LognormalE distribution has as its parameters the mean and standard deviation of the Normal distribution of loge[X].

ModelRisk functions added to Microsoft Excel for the Lognormal distribution to base B

VoseLogNormalB generates random values from this distribution for Monte Carlo simulation, or calculates a percentile if used with a U parameter.

VoseLogNormalBObject constructs a distribution object for this distribution.

VoseLogNormalBProb returns the probability density or cumulative distribution function for this distribution.

VoseLogNormalBProb10 returns the log10 of the probability density or cumulative distribution function.  

VoseLogNormalBFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution.

VoseLogNormalBFitObject constructs a distribution object of this distribution fitted to data.

VoseLogNormalBFitP returns the parameters of this distribution fitted to data.

 

Lognormal distribution to base B equations

 

 

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