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Normal distribution is a probability distribution commonly used in Finance and other social sciences for statistical tests. There are several versions of the normal distribution, but the one called 'standard normal distribution' has a mean of 0 and standard deviation of 1 and is the default used to standardize data in spreadsheets and statistical analysis programming languages.
Synonyms: bell-shaped curve, Gaussian distribution, Gaussian function
For context, the normal distribution is one of several bell-shaped curves. One such distribution, the Student's T-distribution is often used in place of the normal distrbution when modeling stock returns because it reflects more observations in the tails, which is more aligned with historical stock returns.
Also, interestingly, in Excel, you can determine the probability of a
sample value using an alternatively shaped normal distribution. You do this
by supplying the
these four items in succession.
The cumulative distribution function shows the cumulative percentage of the distribution under, or to the left of, the observed value. This is akin to the probability of observations below the value.
So for example, imagine you had 60 monthly returns for each of 100 stocks and the average monthly return was 0.6%. Annualized, this would be about a 7.2% return. The standard deviation of all monthly observations was 5.0%, or an annualized standard deviation of 17.3%.
So to determine the probability of observations below the monthly return of
10.0% using this distribution, in Excel you could input
=NORM.DIST(0.1,0.006,0.05,TRUE) for an
answer of 0.9699. So, to interpret, 97% of observations would be predicted
to fall below a return of 10.0%.
Bud: Guy fails to realize that referring to the
'normal distribution' as 'Gaussian' is off-putting.
Rex: Yeah, classic Quant. Most I know are at least two standard deviations from normal.
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Click box for answer.
False. The t-distribution is better suited for small sample sizes.
True. False returns a probabilty mass function which is better suited for discrete random variables instead of continuous.
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