- #1

- 1,266

- 11

## Homework Statement:

- What is the name of the following distribution, and why does increasing the exponent increase the magnitude variation?

## Relevant Equations:

- Matlab code is shown below.

I have generated a distribution (normalized such that the sum is equal to 1) by using the code:

For an exponent ##z=1##, the sampling distribution is "flat", but it also has a shorter range. Enlarging ##z## gives a wider range of numbers. Why?

Here is a comparison of the results for ##z=1## and ##z=5##:

Also, is it possible to have both a wide range and a "flat" distribution at the same time (i.e. very large numbers being just as likely as the small numbers)?

Explanations would be greatly appreciated.

Matlab:

```
M=500; % Number of samples
z=1;
SUM = 1;
ns = rand(1,M).^z; % random numbers
TOT = sum(ns);
X = (ns/TOT)*SUM; % Re-scaling
hist(X(1,:),100)
```

Here is a comparison of the results for ##z=1## and ##z=5##:

Also, is it possible to have both a wide range and a "flat" distribution at the same time (i.e. very large numbers being just as likely as the small numbers)?

Explanations would be greatly appreciated.