# Compute the kurtosis of standard Gaussian distribution

In this post, we will derive the kurtosis of stand Gaussian distribution

is 3. We use the following equation to calculate the fourth central moment

The fourth central moment is

Therefore, the kurtosis is

For an application of Kurtosis analysis in saliency detection/in-focus segmentation, please refer to our paper and source code.

# Dutch national flag problem – matlab

Dutch national flag problem is a classic programming problem. It groups the input array into three sub-groups in just one pass. For detailed information, please refer to http://en.wikipedia.org/wiki/Dutch_national_flag_problem

```function x = category_sort(x, low, high)

len = length(x);
p = 1; q = len;
i = 1;

while i <= q
if x(i) < low     % move the current element to the front
tmp = x(p);
x(p) = x(i);
x(i) = tmp;

p = p + 1;
i = i + 1;
elseif x(i) >= high     % move the current element to the back
tmp = x(q);
x(q) = x(i);
x(i) = tmp;

q = q - 1;
else    % move to the next element in the array
i = i + 1;
end
end

```

We can test the code by simply running the following script:

```x = 3 * rand(20, 1);
x = category_sort(x, 1, 2)
```