Suppose, I have 25 sample values. I have no idea as to which distribution, the observation comes from. How will I proceed?
With regard to the same question:
Suppose, though I have no idea, I pretend that it comes from normal distribution and estimate its mean and variance, do a P-P or an Anderson-Darling and conclude that it comes from normal density. Precisely, does it essentially mean that the data follows normal distribution. Aren't I just trying to fit my data to a convenient distribution?
In short, given a continuous sample, how do I decide its original parent distribution??
1) Why do you need to know the distribution? What are you really trying to achieve?
2) Failure to reject normality doesn't tell you the distribution is normal. It only tells you your sample was too small to tell the difference.
You can't. But why do you need to?
You might choose an approximate distributional model for some reason or other, or you might be able to proceed with some other form of inference without making any such choice.