Stats question

[bryant]

Is it possible to perform a confidence interval test on data that isn't normally distributed? I've searched the quant methods book and can't find anything pertaining to the matter. Any info is most appreciated. Thanks

 

[ahahah]

bryant Wrote:
-------------------------------------------------------
> Is it possible to perform a confidence interval
> test on data that isn't normally distributed?
> I've searched the quant methods book and can't
> find anything pertaining to the matter. Any info
> is most appreciated. Thanks


sure, you just have to make an assumption regarding how the data is distrubuted which is probably harder if assuming normality is clearly wrong...

 

[dynamic_hedger]

You definitely can. I distinctly remember one of the CFA books mentioning that a distribution with excess kurtosis (i.e, leptokurtic) has wider confidence intervals. A leptokurtic distribution is obviously not normal.

In general, a confidence interval of, say, 95% means the area under the probability density function is 0.95. The precise shape of the distribution should not matter because this condition can still be satisfied.

I suspect you are running into problems because you are thinking of confidence intervals as 1.96 x standard deviation, etc., which is a narrow definition that's only valid for normal distributions.

 

[bryant]

I hate to give you guys the run around because you are very generous with your time, but I have posted more information in the level II forum regarding this problem. If you would like to take a look, that would be wonderful. Thanks

 

[cosine]

Leptokurtic? Wtf?

Bryant, assuming no serial correlation in your sample, you're looking for the 95th percentile. As simple as that.

 

[dynamic_hedger]

The term 'leptokurtic' appears in the CFA Level 1 readings. It was also on the Level 1 exam when I wrote it two years ago (specifically, the question asked if the t-distribution is leptokurtic).