I examine the distribution of some random variables in order to estimate their average value. The sample size is 116 values. Known expectation, variance and other statistical characteristics. It is also established that the three quantities studied are subject to
Generalization of extreme values, Rayleigh distribution and Johnson's SU-distribution laws. I need to determine if my sample size is enough for 116 measurements. Who knows such formulas?
There is a classical book, Sampling Techniques - William G. Cochran. I recomend you take a look.
From a general point of view, consider that the Student's t-variable is enough robust for variables not heavily violating normality. So, if your data distributions are heavily skewed, I cannot help you anymore. Otherwise, if data don't dramatically violate normality, I suggest you to suppose that t-variable t=(mean(x)-E(x))/s/sqr(n) has still a t-distribution. This is helpful: you can find out n, the minimum sample size, which give you an acceptable error of the average. In fact, if D is the maximum acceptable error of (mean(x)-E(x)), from the equation above results that n >= t2Var(x)/D2. So, under the initial hypothesis, you can proceed as follows: calculate the experimental Var(x), select a critical t value (for example t=2 with 95.5% of confidence and infinite d.o.f), choose D that you are ready to accept, and finally calculate n. If it is less than 116 your sample size is fulfilling your acceptability criteria; if it is more than 116 your desiderata cannot be accomplish with this sample size.
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