What I said ,add 01010101.. To when there’s a gap between ether quakes, apply any function to when there’s a quake and when there’s not.

The zero are randomized the data, so add basis.

]]>Thanks again for linking to your python fft code.

I adjusted the array size to the number of minutes in a year, and the lambda argument of expovariate for about the right number of events per year.

The resulting plot is completely level (extremely noisy, but with dense scattering of maxima at the equal strength, independent of frequency). I imagine this is how a white noise spectrum would plot.

For comparison, I tried assigning every member of array X from the random() function. Excepting a small difference in vertical (db) scaling, the plots are qualitatively identical.

I haven’t tested with real-world data, though it’s not obvious to me that the results would be different.

]]>It may be curious to inspect changes in the running Root Mean Square of two or more consecutive event timestamp deltas.

May mean nothing. Just food for thought.

]]>In statistics, the arithmetic average rules. Because it defines the expected value

That is so, but how do we know we are handing the appropriate measurements for our problem to the statistical machine ? The geometric mean can also be regarded essentially as the arithmetic mean, of the logarithm of another quantity. How do we know which to use ?

]]>Setting to one side the question of whether anybody would survive to tabulate the statistics of day with a million strong quakes, I’m dubious that it’s physically possible.

As a humble analogy, the ability to detect 15th harmonics in the spectrum of a square wave does not imply a measure of probability that zero-crossings might occur at 15 times the fundamental frequency.

]]>I’ve been careful to refer to the plot I constructed as a “proxy”, “estimation” or “approximation” … I don’t propose that it’s a proper spectrum!

My intuition is that the actual spectrum would be qualitatively similar, but I won’t know unless I run an actual spectrum, which would take some doing.

Literally, of course, the plot represents a distribution of intervals between successive events in the dataset.

Thanks to FA, for linking the Python code. I haven’t familiarized myself at all with the marvelous population of packages available for Python. From a first glance, it seems that numpy and scipy can do an prodigious variety of computations.

]]>Which suggests the question what is the most appropriate average to use, arithmetic, geometric, harmonic, etc., or does it matter ?

In statistics, the arithmetic average rules. Because it defines the expected value, see https://en.wikipedia.org/wiki/Expected_value.

]]>the average of a set of numbers is not the same the reciprocal of the average of the reciprocals…

Unless it’s the geometric average.

Which suggests the question what is the most appropriate average to use, arithmetic, geometric, harmonic, etc., or does it matter ?

]]>(Continued, trying to explain the suspected flaw in your procedure)

Suppose you see two successive events that are one hour apart. So you say the average rate is 24 / day.

Then you see two successive events that are 6 hours apart, so you say the average rate is 4 / day.

In your scheme, the two get the same weight. But the latter covers a period that is six times longer, so it should get six times the importance of the former in the statistics.

Another unrelated thing to think about: the average of a set of numbers is not the same the reciprocal of the average of the reciprocals…

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