Help with a probability

W

Weatherman

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Hello

I'm trying to calculate the chances of Sydney recording 3 months in a year with a rain record. Here are the details.
Sydney has 164 years of weather data
There are 12 months in a year
3 months this year have broken the record

To break the record in 1 month that's 1-{163}{164}^12 = 0.07076603352

But how do i calculate 3 months in 12 breaking a record?

Cheers in advance if anyone can help me
 
blamocur said:
Do you mean 1-(163/164)^12 ?
Where does this estimate come from ?
Click to expand...
Yes that's what I mean. That's just the probability of selecting 1 number from 164 given 12 chances....but I need to select 3 numbers from 12 chances
 
To make an estimate, you need to know how many months in those 164 years broke the record. You seem to be assuming that only 1 did???
 
Why do you think that the prior 163 years did not have record breaking rain for three month in a year?
 
The first year broke the record every month since its the first year of data. After 163 years of data the chance becomes 1/164 for each month in isolation
 
You need the binomial distribution for a calculation of this type. The chances of an event, with probability "p", happening 3 or more times in 12 trials (months) is...

[math]\sum_{k=3}^{12}\binom{12}{k}p^k(1-p)^{12-k}[/math]
And, IF the probability of breaking the record is p=(12+3)/(164*12) then P(3 or more in 12 trials) ≈ 0.0000925 This value of p assumes the record has only been broken (12+3) times in (164*12) months. I'm highly skeptical of this figure. You told us that the rainfall record was broken 12 times initially, and then this record has stood until this year when it was broken 3 times? This seems very unlikely.

Note: I'm not a climate change skeptic. But, I don't think the above method is the correct approach and I don't think it provides a useful or representative answer. I'd recommend that, instead, you build a histogram of the individual monthly rainfall figures for the last 164 years. Perhaps this data will look like it has a normal distribution. And if it has, then you'd be able to get a much better value for "p", the probability of rainfall exceeding the previously held record.
 
Last edited:
Weatherman said:
The first year broke the record every month since its the first year of data. After 163 years of data the chance becomes 1/164 for each month in isolation
Click to expand...
In order to answer your question (or, really, in order to ask it!), you need to specify a distribution for the random variable (as implied by Cubist). Here is a demonstration of how record-breaking works: https://demonstrations.wolfram.com/RecordsInSequencesOfRandomVariables/

The main thing you'll see is that, of course, when you first start keeping records, you will break records far more often than you will later; the first measurement will by definition be a new record. (It seems unlikely, though, that a record would be broken every month the first year.) Subsequently, it will become less and less frequent; your simplistic calculation is totally inappropriate.

Also, as far as I can tell, you are asking about this probability under the assumption that this distribution is static, perhaps in order to shown that that assumption is unlikely to be true. If the average amount of rainfall is increasing over time, that changes everything; you would need a different kind of model.

Ultimately, you just need a lot more data in order to discuss all this), as well as a lot more theory.
 
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