Daily Archives: January 4, 2013

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;

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

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