Mathematics | Hypergeometric Distribution model

Hypergeometric Distribution Model is used for estimating the number of faults initially resident in a program at the beginning of the test or debugging process based on the hypergeometric distribution. Let $C_i-1$ be the cumulative number of errors already detected so far by $t_1, t_2, ...., t_i-1$, and let $N_i be the number of newly detected errors by time $t_i$.


  1. A program initially contains m faults when the test phase starts.
  2. A test is defined as a number of test instances which are couples of input data and output data. In other words, the collection of test operations performed in a day or a week is called a test instance. The test instances are denoted by $t_i$ for i = 1, 2, . . ., n.
  3. Detected faults are not removed between test instances.

Therefore, from the latter assumption, the same faults can be experienced at several test instances. Let $W_i$ be the number of faults experienced by test instance $t_i$. It should be noted that some of the $W_i$ faults may be those that are already counted in $C_i-1$, and the remaining Wi faults account for the newly detected faults.
If $n_i$ is an observed instance of $N_i$, then we can see that $n_i \leq W_i$. Each fault can be classified into one of two categories:

  1. Newly discovered faults
  2. Rediscovered faults

If we assume that the number of newly detected faults $N_i$ follows a hypergeometric distribution, then the probability of obtaining exactly $n_i$ newly detected faults among $W_i$ faults is,



    $$C_{i-1}= \Sigma_{k=1}^{i-1}n_k, \; C_0=0\; n_0=0 $$


    $$max\{0, W_i-C_{}i-1\}\leq n_i\leq max\{W_i, m-C_{i-1}\}$$

for all i. Since $N_i$ is assumed to be hypergeometrically distributed, the expected number of newly detected faults during the interval $[t_{i-1}, t_i]$ is,


and the expected value of $C_i$ is given by,

    $$E(C_i)=m\left [1- \prod_{j=1}^i (1-p_i)  \right ]$$


    $$p_i=\frac{W_i}{m}\; i=1, 2, ...$$

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using or mail your article to See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.