Write code that performs simulation

Assignment Help Advanced Statistics

Reference no: EM131993113

Homework -

George Marsaglia's Diehard tests are a battery of statistical tests to test the quality of a random number generator (RNG). In this assignment, we will run one of the tests.

The test proceeds as follows: take a cube of size 1000 x 1000 x 1000, and use your RNG to produce 4000 points uniformly distributed throughout this cube. Out of these 4000 points, find the two points that are closest to one another, distance being measured by the usual Euclidean metric. Let r be the distance between these two points, and let V = 4/3πr³. (So V is the volume of the largest sphere which is centered at one of the 4000 points, and which does not contain any of the other points in its interior.)

The variable V should be very close to being exponentially distributed with mean 40π.

Task - Write code that performs this simulation, using each of the following uniform generators (code for which can be found in the template .cpp file that I have provided):

the RANDU generator;
the LCG with a = 22695477; c = 1; m = 2³²;
and the Mersenne Twister.

For each of the three generators, run this simulation 10,000 times. This should produce 10,000 values of V: output each of those 10,000 values into a text file, with a different number on each line. (Use a different file for each of the three generators.)

I have provided starter code in the file sphere template.cpp (see below if you feel more comfortable using Python).

Need code in python.

Attachment:- Assignment Files.rar

Reference no: EM131993113

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Reviews

len1993113

5/23/2018 3:00:06 AM

Subject: Advanced Statistics. Message: I need code in python. Recommended. If you want to see pretty histograms of the data, you'll need a Python interpreter, together with a number of modules installed { the easiest way to obtain this is to just download Anaconda for Python 3.x (go to anaconda.com/download). Open the Anaconda Navigator, then open Spyder, and from there open and run the sphere histogram.py script, inputting the name of one of the files you have generated. If your program runs correctly, you should see that RANDU is garbage, and the other two perform quite well (when I ran it, the Mersenne Twister ws slightly but noticeably better than the other LCG).

len1993113

5/23/2018 3:00:01 AM

Suggestions- this program, if done in the obvious way, is very computationally intensive. Performing 10000 trials takes my computer about 15 minutes. I would start with 100 trials just to make sure your results make sense, before attempting a run of 10000 trials. I think it's a good idea to design a simple class for points in R3, with a method for finding distances between points. Since the code should be exactly the same for all three generators, use UNIF() for your random number generator; you can then simply replace #define UNIF LCGUniform with #define UNIF RANDU Uniform or #define UNIF MTUniform when you want to switch generators.

len1993113

5/23/2018 2:59:56 AM

Further Directions - The most obvious way to calculate the minimum distance among the points is a rather slow algorithm - if there are n points, it takes on the order of n2 steps. There is a faster way to accomplish this - an O(n log n) algorithm. Can you implement that? Also, instead of merely visually confirm that our data fit the purported distribution, there are so-called \goodness of fit" tests which can give more objective answers. Try to implement one of these.

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