PowerLaw | Topcoder Archive

Problem Statement

A power law distribution is one where the probability density of a value X >= 1 being observed in a trial is proportional to X^-a where a is some constant.

We have collected some data from the real world, and we suspect that it comes from a power law distribution as described above. We would like to find the most likely value of a for this data. That is, what value of a in the range above would generate the observed data with the highest probability density.

Definition

Class:: PowerLaw
Method:: fit
Parameters:: double[]
Returns:: double
Method signature:: double fit(double[] x)
(be sure your method is public)

Constraints

The answer will be greater than 1 and at most 1000.
x will contain between 1 and 50 elements, inclusive.
Each element of x will be at least 1 and non-infinite.

Examples

```
{1,1,1,1,2}
```
```
Returns: 8.213475204444817
```
When a=8.213475204444817 the probability density at 1 is 7.21348 and the probability density at 2 is 0.024302. The overall probability density of observing this data from a=8.213475204444817 is 65.7992. It turns out that any other value of a would result in a lower probability density.

{1,1,1,1,2,2,2,3,3,4}

Returns: 2.765860813452108

{1,2,3,4,5,6,7,8,9,10}

Returns: 1.6620581867464064

```
{1,1000}
```
```
Returns: 1.289529654602168
```

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