Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

[Phys-L] Re: For pot watchers: is it a conspiracy?



part II


Prob. of no events in the time interval T during which one would expect
(on average) aT events is

Pzero = exp(-aT), where a is the mean counting (event) rate.


Consider a time interval t w/ no event followed by one event in the time
t + dee t. This combined prob. is:

dee P(of t) = a [exp(-at)] dee t

for a large number of intervals (N), between events, the number of
intervals > Tone, and < Ttwo is

n = N [ exp(-aTone - exp(-aTtwo)], where a, again, is the average
number of events / unit time.

Note the limiting cases: Ttwo => lazy eight and Tone => 0

quoting Evans:

Examples of the usefulness of the interval distribution in ..... and in
cosmic-ray-burst observations will be given in Chap. 27, Sec. 4. A
generalization of the interval distribution, giving the frequency
distribution of intervals which contain any predetermined number of
random events, is derived in Chap. 28, Sec 2.

Also much space is devoted to the related ancient technology of
mechanical counters and counting rate meters.

bc







Bernard Cleyet wrote:

Don't know, however, rather certain one can calculate the rate of such
lacunae.

The time between counts is a simple exponential.

bc, off to find the function for part II; this is part one.

p.s. have not we discussed this before? hint an unfortunate even is
certain to be soon followed by another.

Chuck Britton wrote:

I would like there to be a 'statistic' that could tell us how long we
could 'expect' to wait until a similar 'run' will occur.

Is this reasonable?





On 25-Jul-05 Bernard Cleyet wrote, regarding the remarkable(?) gamma ray
burster lacuna in June and July:



BYes it looks good. However, as one author wrote (paraphrased)
those who
do Chi by eye deserve what they get.

So I tried Pearson's test w/ 42 intervals (single day) and m the
claimed
0.274/day. I should have stopped there, as there are only three
classes
(0, 1, & 2) should be at least 5. Anyway, I found Chi square =
0.52 w/
one deg. of freedom. Using the fig. in Evans (p.776) p= ~ 0.5 i.e.
good agreement w/ Poisson distrib. However, I did violate the
condition.

So I tried three day intervals. This time the data looked bad!,
and Chi
square = 13 w/ three degs. of freedom. p = ~ 0.01 rather unlikely
agreement w/ Poisson distrib. Requirement still not fulfilled, but
more
nearly so.

So "went to" Leigh's reference for more data. Nope. Then I turned
the
page in Evans and found "An Extension of the Chi-square Test" cutting
to the chase, only n need be > 5 (it's 42), and I obtained p ~ 0.2
Again a bit ambiguous as it should be between 0.3 and 0.4

Evidently I've gone wrong; where?

bc, not a statistician

I am not a statistician either, Bernard, and I don't know where you
"went
wrong", except, perhaps, by starting the calculation in the first place.
We all know that the lacuna is an *a priori* improbable event, but so is
winning the lottery.

My purpose was to exemplify the futility of doing *a priori* calculation
on *a posteriori* events. As I said, I know we all do it, and since this
one happened to my son, I knew about it during the scary period when the
Swift team, understandably, worried about the health of their
instrument.

Taking such a calculation seriously could lead only to one's
entertaining
hypotheses like "The Universe is trying to tell us something" and other
scientifically heretical ideas. It is equivalent to reestablishment of a
geocentric cosmology.

Science, whether we like it or not, is a faith-based culture. If atheism
is not quite compulsory for a scientist, there is tacit agreement
that we
will accept no scientific hypothesis that invokes gods as mechanism*. We
do not believe in miracles, and the justification for our faith lies in
probability calculations based upon large experiential data bases which
demonstrate time after time that miracles are based upon myopia, the
failure to observe a sufficiently large data base. This is particularly
dramatic when one is in the midst of a heat wave, as I know some of you
are. As hot as it is, and as little as it helps to know it, your weather
is not unprecedented.

Leigh

*"deus ex machina"



_______________________________________________
Phys-L mailing list
Phys-L@electron.physics.buffalo.edu
https://www.physics.buffalo.edu/mailman/listinfo/phys-l