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How odd is a cluster of plane crashes?

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Re: How odd is a cluster of plane crashes?

#11

Post by kcorbitt »

phantom784 wrote: post #9

"If there is a crash on 1 August, the chance that the next crash occurs one day later on 2 August is 1/365. But the chance the next crash is on 3 August is (364/365) x (1/365), because the next crash occurs on 3 August only if there is no crash on 2 August." Is this not the gambler's fallacy? Shouldn't the odds be unaffected by a previous crash?

You're right that the probability that there is a crash on 3 August is unaffected by a potential crash on the 2 of August, but the chance that the crash on the 3 of August is the next crash (after the 1st of August) is affected.

Re: How odd is a cluster of plane crashes?

#12

Post by DanBC »

dmichulke wrote: post #3
simonh wrote: post #2

One of the first computer programs I ever wrote just put random dots on a screen and I remember looking at how 'lumpy' the results were. Intuitively most people assume that random distributions will be even distributions, but in fact they are usually full of clusters. Some mathematicians can reliably distinguish 'random' sequences created by people from truly random ones because people produce distributions that are…

I don't disagree at all and I remember seeing studies or articles writing about that phenomenon. Just wanted to add that a few years ago (when you wrote your first computer program) a randomly selected random number generator was more likely to be less random than a randomly selected random number generator today.

Early random number generation was terrible. You wouldn't get clumps / no clumps, you'd get fuzzy straight lines.

Re: How odd is a cluster of plane crashes?

#13

Post by philh »

kcorbitt wrote: post #11
phantom784 wrote: post #9

"If there is a crash on 1 August, the chance that the next crash occurs one day later on 2 August is 1/365. But the chance the next crash is on 3 August is (364/365) x (1/365), because the next crash occurs on 3 August only if there is no crash on 2 August." Is this not the gambler's fallacy? Shouldn't the odds be unaffected by a previous crash?

You're right that the probability that there is a crash on 3 August is unaffected by a potential crash on the 2 of August, but the chance that the crash on the 3 of August is the next crash (after the 1st of August) is affected.

Also, pedantically, a plane that crashes on the 2nd August isn't going to crash again on the 3rd.

We can reduce the rate of crashes by taking planes out of the sky, and one way to do that is to crash them.

Re: How odd is a cluster of plane crashes?

#14

Post by redcalx »

philh wrote: post #13
kcorbitt wrote: post #11

Earlier quoted context omitted.

You're right that the probability that there is a crash on 3 August is unaffected by a potential crash on the 2 of August, but the chance that the crash on the 3 of August is the next crash (after the 1st of August) is affected.

Also, pedantically, a plane that crashes on the 2nd August isn't going to crash again on the 3rd. We can reduce the rate of crashes by taking planes out of the sky, and one way to do that is to crash them.

Unless there are reserve planes that come immediately on-line to fill the gap (or the remaining planes do more fly time).

Re: How odd is a cluster of plane crashes?

#15

Post by mungoman2 »

martin-adams wrote: post #8
simonh wrote: post #2

One of the first computer programs I ever wrote just put random dots on a screen and I remember looking at how 'lumpy' the results were. Intuitively most people assume that random distributions will be even distributions, but in fact they are usually full of clusters. Some mathematicians can reliably distinguish 'random' sequences created by people from truly random ones because people produce distributions that are…

I do wonder if that is down to sample size. For example, I wrote a program to simulate the roll of a dice. There is a one in 6 chance of getting any one number. But roll it 6 million times, you'll be very close to have each number 1 million times. So I would anticipate the clumping to even out as the sample size increases. Or maybe the evening out is a large collection of clumps. Anyone know if this is the correct wa…

Well depends of what you mean by very close. It's the relative numbers that approaches the true distribution, not the absolute numbers.

Do the experiment you decribe and look at the numbers.

Re: How odd is a cluster of plane crashes?

#16

Post by Osmium »

martin-adams wrote: post #8
simonh wrote: post #2

One of the first computer programs I ever wrote just put random dots on a screen and I remember looking at how 'lumpy' the results were. Intuitively most people assume that random distributions will be even distributions, but in fact they are usually full of clusters. Some mathematicians can reliably distinguish 'random' sequences created by people from truly random ones because people produce distributions that are…

I do wonder if that is down to sample size. For example, I wrote a program to simulate the roll of a dice. There is a one in 6 chance of getting any one number. But roll it 6 million times, you'll be very close to have each number 1 million times. So I would anticipate the clumping to even out as the sample size increases. Or maybe the evening out is a large collection of clumps. Anyone know if this is the correct wa…

> So I would anticipate the clumping to even out as the sample size increases.

Clumping won't even out. A useful way of thinking about it is in terms of the distance between samples (e.g. a radial distribution function). If you don't have clumping, that distribution of distances is decidedly non-random and has peaks. Additionally, there's no specific length-scale for the clumping to happen on, it's essentially fractal in nature.

(Happy to be corrected if I'm wrong on this.)

Re: How odd is a cluster of plane crashes?

#17

Post by martin-adams »

mungoman2 wrote: post #15
martin-adams wrote: post #8

Earlier quoted context omitted.

I do wonder if that is down to sample size. For example, I wrote a program to simulate the roll of a dice. There is a one in 6 chance of getting any one number. But roll it 6 million times, you'll be very close to have each number 1 million times. So I would anticipate the clumping to even out as the sample size increases. Or maybe the evening out is a large collection of clumps. Anyone know if this is the correct wa…

Well depends of what you mean by very close. It's the relative numbers that approaches the true distribution, not the absolute numbers. Do the experiment you decribe and look at the numbers.

This is what I mean:

  var results = [0,0,0,0,0,0];
  for (var i = 0; i
The results are:

  [1002140, 999355, 1000009, 1000401, 1000014, 998081]
Basically, they are all within 1% tolerance of each number getting 1 million occurrences.

So when you look at the clumping on random dots on a screen, given a large enough sample size, I would anticipate that the probability of keeping a clumped visual distribution would become quite improbable.

Re: How odd is a cluster of plane crashes?

#18

Post by leni536 »

simonh wrote: post #2

One of the first computer programs I ever wrote just put random dots on a screen and I remember looking at how 'lumpy' the results were. Intuitively most people assume that random distributions will be even distributions, but in fact they are usually full of clusters. Some mathematicians can reliably distinguish 'random' sequences created by people from truly random ones because people produce distributions that are…

An other great example is how random is a terrible algorithm for dithering.

https://en.wikipedia.org/wiki/Dither#Algorithms

Re: How odd is a cluster of plane crashes?

#19

Post by leni536 »

phantom784 wrote: post #9

"If there is a crash on 1 August, the chance that the next crash occurs one day later on 2 August is 1/365. But the chance the next crash is on 3 August is (364/365) x (1/365), because the next crash occurs on 3 August only if there is no crash on 2 August." Is this not the gambler's fallacy? Shouldn't the odds be unaffected by a previous crash?

In probability you have take attention to the very details. The statements "the next crash occurs on 3 August" and "there is a crash on 3 August" are not the same. Only the latter is independent from a crash on 2 August.

Re: How odd is a cluster of plane crashes?

#20

Post by ijager »

martin-adams wrote: post #17
mungoman2 wrote: post #15

Earlier quoted context omitted.

Well depends of what you mean by very close. It's the relative numbers that approaches the true distribution, not the absolute numbers. Do the experiment you decribe and look at the numbers.

This is what I mean: var results = [0,0,0,0,0,0]; for (var i = 0; i The results are: [1002140, 999355, 1000009, 1000401, 1000014, 998081] Basically, they are all within 1% tolerance of each number getting 1 million occurrences. So when you look at the clumping on random dots on a screen, given a large enough sample size, I would anticipate that the probability of keeping a clumped visual distribution would become qui…

I think the clumping is more about how many consecutive same numbers there are in the array.

For example, a naive me would generate: [3,4,5,1,2,4,2,1,2,6] whereas a true random distribution might generate: [3,4,4,4,4,1,2,2,2]. When you generate 6 million samples you would indeed have about 1 million per number. However you would still have subsequences of the same number.

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