Normal Distribution

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Hi David,

2004 past year question.
This statement is true ------"A symmetric distribution with 6% of area under the curve falling more than 2 std deviation from the mean has fatter tails compared to the normal distribution."

Explanation offered in the answer: a normal distribution has only 5% of area under the curve falling 2 std deviation from the mean.

Can you please explain further on this? I have problem of understanding this concept "6% greater than 5% is fat tail"

Regards
Learning

 

[David Harper CFA FRM]

Hi Learning,

A two-tailed 95% confidence interval for the standard normal distribution is given by -1.96 to +1.96
i.e., = NORMSINV(2.5%) = -1.96 which means that 2.5% is in the left tail when the deviate = 1.96.
2.5% in the left tail and 2.5% in the right tail for a total of 5%

compared to this alternative distribution which has 6% in the tails: since symmetrical, 3% in left and 3% in the right tail
and this is the very defintion (this is the best definition!) of heavy tail: higher probability (3% versus 2%) of a tail outcome

David