Best two PRNG for calculators

[Namir]

(08-30-2014 11:38 PM)Paul Dale Wrote:  Care to elucidate on your methodology for testing these for randomness?
There is a mass of statistical literature and tests available for doing just this.
- Pauli

I am aware that there is a massive suite of tests. I chose a subset of tests for a variety of reason (not to mention time, practicality, and not being paid to do this). I use Excel (and Excel VBA code) to test PRNG functions in groups of 8. I perform the following steps:

1) Generate 32 runs for each PRNG function.
2) Each run generates 100,000 numbers.
3) I calculate and observe the following statistics for each 100,000 numbers:
a. The mean value.
b. The standard deviation.
c. The auto-correlation for the first 30 lags. I record the minimum value, maximum value and sum of the auto-correlations.
d. The Chi-square stat for the histograms with bins of 0.1 size. The ideal value for each bin is 1000.
e. The Chi-square stat for the histograms with bins of 0.05 size. The ideal value for each bin is 500.
4) I calculate an empirical factor based on the mean, standard deviation, minimum auto-correlation, maximum auto-correlation, sum of auto-correlations, Chi-Square for the 10-bins histogram data, Chi-Square for the 20-bin histogram data. The empirical factors tend to penalize a run of random numbers for deviating from expected values.
5) I rank the results based on the empirical factors, seeking the smallest rank values. I calculate the mean, standard deviation, minimum, maximum, and confidence interval for the 32 factor values for each PRNG function.
6) I select the minim mean factor value.