Suggestions: How to write a report about a simulation experiment

Every research report has its own set of ideal formats, depending on the reported experience, the salient features and conclusions, etc. It would be interesting, though, to try to design our reports in a more or less standard and accepted form.

The main idea related to a simulation report is that the experience is nothing but a numerical experiment, in the same fashion as an experiment with animals, crops, etc. Some readers might be tempted to validate the results, or to repeat the experience, and the report must supply all the relevant information in order to help them. It is therefore a must to explicitely state the following items:

• Computer used (type, model, etc.)
• Operating system (UNIX, DOS, VM, etc. including version).
• Computational packages (SAS, S-PLUS, SOC, STATGRAPHICS, etc.)
• The programming language used in the development of the experimenter's programs (FORTRAN, C, PASCAL, etc.) and compiler (MICROSOFT, LAHEY, TURBO-PASCAL, etc.)
• Numerical subroutines involved in the calculations, including their origin or informing about the implemented algorithm(s). If their numerical precission and other details are known, state these facts.

Specifically related to the simulation, report the following:

• Pseudorandom uniform random number generator: type, tests results, either if it is a built-in subroutine of the programming language or not, seeds used, etc.
• Nonuniform pseudorandom number generators: the same as above; also state the algorithms or subroutines used.
• Results about the statistical quality of the pseudorandom sequences that will be involved in the study if any (there always should be).

In a forthcoming Section we recall a format for the report itself, suggested by Lewis and Orav (1989). This is neither the best nor the only possible form; again, every problem is a problem in its own right, but it might be useful to consider it as a reference.

Notation: For every we denote its integer part as , i. e., . Let be a real-valued vector. The evaluation of some of the following quantities will be called the analysis of the empirical distribution of .

1. Sample mean of .
2. Sample variance of .
3. Standard deviation of .
4. Sample skewness of , where

   

5. Sample kurtosis of , where

   

6. Sample mean variance of .

Let now be the vector sorted in ascending order. We write (i. e. ).

1. Sample median of

   

2. Sample lower quartile of

    

3. Sample upper quartile of

    

In formulas (1) and (2) we wrote:

Let be a constant such that , we then define the

1. -sample quantile of

   

2. Sample coefficient of variation of .

A fairly complete summary of the relevant properties of the aforementioned quantities, when is a random vector such that are the outcomes of independent identically distributed random variables, can be seen in Lewis and Orav (1989).

In the next Section we shall show how the previous suggestions could be applied to a problem of Image Processing: a Monte Carlo study that aims at comparing certain statistical procedures for estimating the parameter of a Rayleigh distribution. We will consider this distribution under a pure and a contaminated model. This kind of estimation problem appears in the statistical treatment of Synthetic Aperture Radar (SAR) images.