Generate random lognormal distributed numbers

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Aboozar Garavand 2017-3-22

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https://ww2.mathworks.cn/matlabcentral/answers/331261-generate-random-lognormal-distributed-numbers

评论： the cyclist 2017-3-22

How I can generate random lognormal distribution data,on the range of [2000 2500] with the mode of 2400?I dont have the quantities of mean and standard deviation!

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Torsten 2017-3-22

It is obvious that one parameter (mode) cannot be enough to substitute two parameters (mean and standard deviation)...

Best wishes

Torsten.

Aboozar Garavand 2017-3-22

How I can generate lognormal distributed data on this range,with negetive skewness ??

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Answer 1

the cyclist 2017-3-22

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编辑：the cyclist 2017-3-22

在 MATLAB Online 中打开

The mode of a lognormal is

exp(mu-sigma^2)

where mu and sigma are the location and scale parameters. It looks like you will have an infinite number of choices available to you, to make the mode equal to 2400.

Next, you ask for the distribution over a finite range. Well, the lognormal has an infinite range. So, you could just remove values outside that range -- but then the remaining values will no longer be strictly lognormally distributed.

So, what you are asking for isn't strictly possible. You have some decisions to make. Maybe after you have made those decisions, you can use lognrnd (from the Statistics and Machine Learning Toolbox) to generate some random draws.

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Aboozar Garavand 2017-3-22

编辑：Aboozar Garavand 2017-3-22

Thank you very much.you are absolutley right!some values go outside of range in lognormal distribution.as a last question,I am trying create random lognormal distribution that 98% of values located within range of [2000 2500] with most likely value of 2400. is this generally possible using matlab or other statistical softwares?

the cyclist 2017-3-22

在 MATLAB Online 中打开

It may be theoretically possible, but you are starting to put several constraints in place, and I'm not sure if they can all be met.

You can use logninv to calculate the inverse CDF of the lognormal. You'll need that find values of mu and sigma such that

mode = exp(mu-sigma^2)

is equal to 2400, and

lower_x = logninv(lower_percentile,mu,sigma)
upper_x = logninv(upper_percentile,mu,sigma)

where

   lower_x = 2000
   upper_x = 2500
   upper_percentile - lower_percentile = 0.98

All that might be possible. It looks to me that this is three constraints, with three free parameters. But there is also an implicit range on the percentiles, so I am starting to think you cannot actually achieve everything you want.

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