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If annual snowfall is Gumbel distributed, show that the snowfall over n years is also Gumbel...

If annual snowfall is Gumbel distributed, show that the snowfall over n years is also Gumbel distributed.

Math   Statistics-And-Probability   
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Answer #1

The cumulative distribution for gumbel distribution is

  where is the mean and is the standard deviation.

Since each year the snowfall is Gumbell distributed, so

, i = 1,2,...n

Since all the years are independent, therefore

which is the cumulative distribution function of gumbel distribution over n years.

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