Sampling distribution of log normal distributions

[David C. Howell]

My daughter just asked me a question that I should be able to answer, but can't. Any help would be appreciated.

It is well know that the sum of normally distributed random variables is itself normally distributed. But I want to know the sampling distribution of the sum of lognormal distributions.

My first thought would be that the central limit theorem would suggest that the sampling distribution would approach normal as N increases. On the other hand, when I generate multiple independent lognormal distributions and then take their sum, a P-P plot tells me that the sum is nicely lognormal, not normal.

Any suggestions?

Thanks,
Dave Howell

                                                                                                                                     

David C. Howell
Professor Emeritus
University of Vermont

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David C. Howell                                 Phone: (970) 871-4556
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