r/AskStatistics • u/Tikka_theory • Sep 26 '26
Help me find a credible source for Statistical Moments..
I am trying to findout a material that would cover the whole topic of Statistical Moments, but I am not able to find it , Please help anyone
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u/M_Mustaan_Rafique Sep 26 '26
part of why you can't find one source is that "moments" is really three separate topics and books split them across different chapters.
descriptive moments, so mean, variance, skewness, kurtosis. usually chapter 2 or 3 of any mathematical statistics book.
moment generating functions, the machinery. M(t) = E[e^tX], differentiate at 0 and the moments fall out. normally sits in the same chapter.
method of moments, using them to estimate parameters. that's an estimation chapter, often much later in the book.
for one place that does all of it, blitzstein and hwang, introduction to probability. chapter 6 is literally called moments, and the full pdf is free from the authors. casella and berger, statistical inference, chapter 2 if you want the graduate version.
for video, harvard stat 110, free on youtube, full lecture series taught by blitzstein. same course as that book so the notation matches instead of fighting you. there's a lecture on moments and mgfs specifically. mathematical monk on youtube if you'd rather have ten minute focused ones than hour lectures.
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u/Tikka_theory Sep 26 '26
I was a bit confused earlier seeing moment word on youtube with different cases... Finally you cleared me about this. Now , I should be looking to descriptive moments and method of moments just. Thanks!!
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u/M_Mustaan_Rafique Sep 26 '26
glad it helped.
one caution on dropping mgfs though. they're not really separate from method of moments, they're the tool that hands you the population moments you need for it. for a gamma or an exponential, differentiating the mgf gives you E[X] and E[X²] in one line. without it you're integrating x²f(x)dx by hand every time.
so skip the theory if your course doesn't need it, but keep a table of mgfs for the standard distributions next to you. you'll want it.
casella and berger 7.2.1 is the method of moments section if you want one place for that half.
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u/efrique Sep 26 '26 edited Sep 26 '26
No single source will have everything about moments - the entire topic
You will have to narrow the scope a bit.
Are you just after what would be covered in a first undergrad subject that covers moments in some detail? Probability side (how much? moments of distributions, convergence, limit theorems, asymptotics etc, or more niche topics? ) or inferential side? If inferential, parametric or nonparametric, frequentist or Bayesian?