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DATA > RANDOM > MATRIX

PURPOSE Generate matrices where the cell values are drawn randomly from a variety of possible distributions.

DESCRIPTION Generate a set of m´n matrices whose elements are random numbers drawn from any of the following distributions - uniform, normal, binomial, Poisson, gamma or exponential.

PARAMETERS
# of rows: (Default = 10).
The number of rows in the random matrix to be generated.

# of columns: (Default = 10).
The number of columns in the random matrix to be generated.

# of levels: (Default = 1).
The number of matrices to be generated, all matrices will be of the same dimension.

Probability distribution: (Default = Uniform).
The underlying distribution from which the elements of the matrix are taken. 

Choices are: 
 
Uniform 
Each cell value is taken from a [0,1] uniform distribution so that each cell value is between 0 and 1.  The mean is 0.5.

Normal 
Each cell value is taken from a normal distribution. 
 
Upon execution of the routine with this option a new window will appear with the following parameters:

Mean of normal distribution (Default = 0.0) 
    
Standard deviation of normal distribution (Default = 1.0).

Binomial
Each cell is filled with the number of times an event with probability p occurs in n trials.

Upon execution of the routine with this option a window will appear with the following parameters:

Event probability: (Default = 0.5)
This gives the probability p of success, i.e. the probability of an event occurring during one trial.

# of trials (Default = 1).
This gives the desired number of repeated trials n. The mean is np.

Poisson
Each cell is filled with the number of times an event occurred in a unit interval of time assuming a Poisson process. 

Upon execution of the routine a window will appear with the following parameter:

Average # of occurrences per time period (Default = 1.0).
This gives the mean of the distribution.

Gamma
Each cell is filled with the time taken for the kth occurrence of an event to occur assuming the event follows a Poisson process with an average of one occurrence per time period. 
   
Upon execution of the routine a window will appear with the following parameter:

  Desired # of occurrences (Default = 1).
  The number k of events which must occur.  The value k=1 gives the exponential distribution. The mean is k.

Exponential 
Each cell is filled with the time taken for the 1st occurrence of an event to occur assuming the event follows a Poisson process with an average of one occurrence per time period. The mean is 1.

Include diagonal values: (Default = YES).
NO will give missing values on the main diagonal.

Generator Seed: 
A seed for random number generator.  Use of the same number will create exactly the same 'random' matrix twice.  Any value from 1 to 32000 is permissible. The default is randomly generated.


  Output dataset: (Default = 'Random').
  Name of data file which will contain random matrix.


LOG FILE  Generated random matrix.  The cells of the random matrix will be of the following type:

UNIFORM - real range [0,1].
NORMAL - real range (-¥,¥).
BINOMIAL - integer range [0,¥).
POISSON - integer range [0,¥).
GAMMA - real range (0,¥).
EXPONENTIAL - real range (0,¥).

TIMING O(N^2).

COMMENTS None.

REFERENCES None.