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Random integral numbers based on normal distribution
Course:- PHP Web Programming
Reference No.:- EM13502




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Your task is to realize two additional data generation functions. Firstly, extend the system to generate random integral numbers based on normal distribution. You need to study Data Generator's structure and extend number generation type to activate normal distribution. The interface needs to obtain both mean and sigma as shown in Figure. Consider the code found 

coding.derkeiler.com/Archive/PHP/php.general/2007-12/msg00317.html

Notice that the return value of the above code is a floating value. You can round it to nearest integer by adding a "rounding option" to the interface.

1081_Random integral numbers based on normal distribution.png

Next, realize one form of skewed distribution that approximates Pareto Principle. Consider a skewed access pattern often evidenced in data applications such that s percent of accesses would go to (100 - s) percent of data items. For instance, a typical "80-20 rule" for 1000 accesses over 500 data items means that about 800 accesses (80% of accesses) go to a specific set of about 100 items (20% of data items). In our case, data generation should be based on independent repeated trials, not as all trials once in a batch. Hence, implementing strict Pareto Principle is difficult. Instead, we can approximate access pattern generation by the following method:

  • skew generation function receives a range r and a skew factor s as parameter, both of which are integers and r must be larger 1 while s must be between 50 and 100.
  • data elements are considered to have unique IDs in the range [1, r], in which elements are listed in an increasing order of IDs such as 123, ..., r.
  • skew generation function produces an integer value between 1 and r representing a data access in the following manner:

1. skewed access will go to the top portion of the elements, that is, those between 1 and t = r × (100 - s) / 100.

2. draw a random number p from uniform distribution between 0 and 99.

3. if p falls in less than s, i.e., [0, s - 1], the top portion of elements [1, t] is accessed.

4. otherwise the access goes to [t + 1, r].

Above illustration should be sufficient to provide you with the concrete requirement for the two frequently utilized data generation. Figure 1 and 2 shows interface and sample output respectively. In these figures, rounding to integer is applied automatically. A checkbox should be added to the interface so that users can choose whether values generated are rounded or not. Notice that this development is not from scratch, but is "reverse engineering" of already developed product. Addition of the above functions to Data Generator is easily done. You should look into the contents of docs/data_type.php.

573_Random integral numbers based on normal distribution1.png

The second task is to add more generation capabilities and/or tailor the built-in functionality of generator. This enables you to produce "all" the test data for the MySQL tables you produced in the previous assignment. You do not need to populate data to the tables in this assignment (which will be the task in the next assignment) but you must become able to generate all the realistic data required for the proposed information analysis. You are not allowed to use other software tools (such as Microsoft Excel) to generate data. You are not allowed to use "existing data" to skip this assignment. Any non-trivial extension from the statistical viewpoint concerning the data nature (like the above assigned functionality) will receive extra credit.




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