# Normal distribution

1. Feb 2, 2012

### Mark J.

Hi.
I need some arguments to move forward the hypothesis that my data are normally distributed.
Except fact that I build histogram and it is similar of shape as normal distribution how can I find some other math arguments (I mean interpreting the logic of normal distribution) to argue about this hypothesis before beginning hypothesis testing with different criteria and tests?

Regards

2. Feb 2, 2012

### Stephen Tashi

One common explanation for a phenomena producing a normal distribution is that it the sum (meaning literally an arithmetic sum) of many independent random random variables.

A hazier philosophical version of this is reasoning is that a phenomena that results from the combined effect of many small and independent random causes will have a normal distribution. (This argument is too vague to be tested mathematically, but you haven't made it clear what kind of "justification" for a normal distribution you want.)

3. Feb 2, 2012

### Mark J.

I have a process of bus arrivals.
While taking inter-arrival times between 2 following buses as random variables I build histogram and it has shape of normal distribution but meanwhile it is similar to log-normal ,etc.
Now I am in search of some math arguments (theory)to check in order to follow the hypothesis of normal distribution.
If you can advice me on that pls

4. Feb 2, 2012

### SW VandeCarr

There are a number of tests of normality. You can directly evaluate the third and fourth moments (skewness and kurtosis) which both should be close to 0. In addition there are specific tests which you can look up: Kullbach-Leiber distance, Kolmogorov-Smirnoff (adaption), Agostino's K squared test, Anderson-Darling, Shapiro-Wilks and tests in SPSS and other statistical software.

http://webspace.ship.edu/pgmarr/Geo441/Examples/Normality Tests.pdf

Last edited: Feb 2, 2012
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