percentile-seeking d-multiple estimate

For two defined gamma distributions with equal expected values, many two-sample random drawings can be done, sample averages calculated from them and ultimately their difference. This is one realization of this difference expression. Doing so many times (here ten thousand times for the given distributions and sample size), many realisations are available, enough to estimate properly the distribution of the sample average difference under the null hypothesis: the two gamma distributions have the same expected values. Once the distribution is available, its 2.5 % and 97.5% p percentiles are available and thus also the multiple d in the equation p = d * (square root of the true variance of the difference of the two sample averages). If d does not fluctuate much, it can be used in practice to calculate back the percentiles (with an estimate of the square root), regardless of the form of the gamma distributions. If such percentiles are at hand, they can be used for testing the null hypothesis in practice. The dataset item contains files, such as "d_sc3_30.xls". The file name means that it concerns sample sizes of 30 and various combinations of the two gamma distribution parameters (the combinations belong to scenario 3 - see below), and the file contains the d multiple estimates for each parameter combination within the scenario. There is the "d_lower", which is the multiple leading to the 2.5% percentile, and "d_upper" leading to the 97.5% percentile.The scenarios are: scenario 1 ..both shape parameters are 1..10, scenario 2..both shape parameters are 11..20, scenario 3.. both shape params are 21..30, scenario 4..shape 1 is 1..10, shape 2 is 11..20,scenario 5..shape 1 is 1..10, shape 2 is 21..30, scenario 6..shape 1 is 11..20, shape 2 is 21..30. The scale 1 parameter is always 1..30. The scale 2 parameter is such that both distributions have the same expected values. Returning to the example "d_sc3_30.xls", this file contains d's for shape 1 = 21 = shape 2, scale 1 = 1, shape1 = 21, shape2 = 22, shape1=21, ..., shape1 = shape2=30, scale1=30. Each row in the file has the d_ lower and d_upper for one of these combinations, and the sample sizes are both always 30.