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1) Suppose, I have 25 sample values. I have no idea as to which distribution, the observation comes from. How will I proceed?

2) 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??

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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.

In short, given a continuous sample, how do I decide its original parent distribution??

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.

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  • $\begingroup$ When you do not need to know the distribution, then why do you have so many distributions to go ahead with estimation and inference? $\endgroup$
    – Vani
    May 14, 2014 at 9:59
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    $\begingroup$ I may be prepared to assume a distribution in various situations, and to check it for plausibility, but in real data analysis, I don't recall ever knowing the actual distribution. $\endgroup$
    – Glen_b
    May 14, 2014 at 10:23

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