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that's really weird. I'm not an astronomer so I thought "hmmm, what's the first thing I can think of in astronomy." Well, how about the magnitude of stars. S
by logicallee 9y ago
that's really weird. I'm not an astronomer so I thought "hmmm, what's the first thing I can think of in astronomy."
Well, how about the magnitude of stars. So, is the magnitude of stars normally distributed? I googled "distribution magnitude of stars" and got images (by clicking on images tab) that seem pretty normally distributed to me. Aren't they?
- pishpash 9y agoFirst sentence on Wikipedia: "In astronomy, magnitude is a logarithmic measure of the brightness of an object..."
- privong 9y ago> First sentence on Wikipedia: "In astronomy, magnitude is a logarithmic measure of the brightness of an object..." That doesn't tell you whether the magnitudes are normally distributed though. That just tells you how the magnitude is computed from an object's observed/measured flux.
- pishpash 9y agoI'm explaining why magnitude looking normally distributed doesn't contradict the parent.
- felippee 9y agoYou mean like this one? http://www.astro.yale.edu/astrom/spmcat/histov.html http://www.astro.yale.edu/astrom/spmcat/histov.html Not really. Plus keep in mind magnitude is a logarithmic measure. Things get skewed when you take logarithms. Also if you look for example at star sizes: http://spiff.rit.edu/classes/phys440/lectures/size/diam_hist_closeup.gif http://spiff.rit.edu/classes/phys440/lectures/size/diam_hist... (from http://spiff.rit.edu/classes/phys440/lectures/size/size.html http://spiff.rit.edu/classes/phys440/lectures/size/size.html). The distribution is certainly not gaussian, and very much likely heavy tail.
- teraflop 9y agoNot to mention that the distributions from three different sky surveys (in your first link) look dramatically different. Which means the histograms are saying at least as much about the measurement process as they are about what's actually out there in the universe.
- privong 9y agoTo add to that, the sharp cutoff at faint (large number) magnitudes is almost certainly a reflection of the fact that astronomical surveys and images have a flux limit, below which objects cannot be individually detected.
- jackpirate 9y agoI think you're being downvoted a bit unfairly. What most non-statisticians don't realize is that some of the most "unnormal" distributions actually look pretty normally distributed, and some of the most ugly looking distributions actually behave like a normal distribution. When you look at a distribution's pdf, you're only looking at the "center" of the distribution. But what statisticians (usually) care about are the tails of a distribution. Consider the following example: The [Cauchy distribution](https://en.wikipedia.org/wiki/Cauchy_distribution https://en.wikipedia.org/wiki/Cauchy_distribution) is a pathological example of a distribution with very heavy tails. Heavier than the power law distributions meantioned in the GP. So heavy, the distribution doesn't even have a mean value. But if you just look at the pdf, it looks almost exactly like a gaussian.
- logicallee 9y agothanks! Very interesting. Is the standard deviation still useful for some of the other distributions you mentioned, that look vaguely Gaussian?
- thanatropism 9y agoThe standard deviation is defined as E[(X-EX)^2] If EX = infinity but X is finite with prob > 0, the standard deviation will be infinite too.
- R_haterade 9y agoYou're referring to the square root of the second moment about the mean. The short answer is yes, it's always useful, provided you have an estimator. Check out Chebyshev's inequality. Just don't start talking about it to your pointy-haired boss. You'll get fired.
- logicallee 9y agothanks. but what does your last line, about the boss mean?
- 9y ago