Analytic algebraic expression of serial data having random pattern

[atisdmitra]

I have conceptualized a method for generating serial binary data at rates varying randomly. This concept should be able to provide data at random rates with various characteristics.The most relevant application is generation of Random sensor data for testing C4I systems (Surveillance and monitoring) before productionising .Some of the statistical parameters characterizing the random data rate are as thus:
i)Ratio of peak value & average value
ii)Ratio of average and variance
iii)Percentage of time instantaneous value exceeds the average value
Is there any possibility of evolving analytical algebraic expression of binary data having such statistical characteristics?
This expression if possible to be evolved can be used to develop an analytical model for a computer communication network for C4I systems .
Through this forum I solicit comments and suggestions of other researchers.
Atis D Mitra

 

[Stephen Tashi]

.Some of the statistical parameters characterizing the random data rate are as thus:
i)Ratio of peak value & average value
ii)Ratio of average and variance
iii)Percentage of time instantaneous value exceeds the average value

How do you define the "average" or "variance" for this case? You'd have to specify a length of time or say that you mean "the average over a time interval as the length of the interval approaches infinity".

You say you want to generate random data "rates". A "rate" would refer to how rapdily data is trasnmitted. The "average" of a binary stream of bits would also depend on the values that are transmitted. You haven't specified whether your "average" refers to the raw value of the bits (i.e. is the average of 011010 = 0.5 ?) or whether the data encodes numerical values (e.g. 011 = 6 ).

If the data is arriving at a constant frequency, I suggest that you look at a simple time series model, such as an "autoregressive moving average model". The statistics of such a model can be calculated analytically. However, I don't know if you can adjust i),ii) and iii) independently of each other in such a model.