There are several goodness of fit tests, may be chi-squared is most famous one, however it seems it is not a preferable choice to be used in the case of continous variables. There is an excellent discussion here: Goodness-of-Fit for continuous variables

I wonder is there any specific suggestion in of normal distribution:

Question: What criteria to use for goodness-of-fit test for normal distribution ?

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    $\begingroup$ This answer gives good advice on normality testing. If testing is appropriate, the choice of test depends rather on the kind of departure from normality you're interested in picking up. $\endgroup$ Jun 26 '18 at 12:23
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    $\begingroup$ I'd also suggest reading Is normality testing essentially useless?; in particular, if you're testing assumptions of some other procedure, I'd point you to Harvey Motulsky's answer there. If you have a good reason to test normality (there aren't many of those but they do come up sometimes), then there are some tests with fairly good power against a range of alternatives, ... ctd $\endgroup$
    – Glen_b
    Jun 26 '18 at 12:35
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    $\begingroup$ ctd... (the Shapiro-Wilk is popular, and a perfectly good choice, though the Chen-Shapiro is a bit better vs a fair number of alternatives) but if you have specific alternatives you want to be sure you have good power against, it's best to tailor the choice of test toward them. $\endgroup$
    – Glen_b
    Jun 26 '18 at 12:35

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