Comments - The law of series: why 4 plane crashing in 6 months is a coincidence - Data Science Central 2021-05-13T04:08:41Z https://www.datasciencecentral.com/profiles/comment/feed?attachedTo=6448529%3ABlogPost%3A189743&xn_auth=no Thanks for this interesting a… tag:www.datasciencecentral.com,2016-03-19:6448529:Comment:403018 2016-03-19T18:58:42.569Z Benoit Lamarsaude https://www.datasciencecentral.com/profile/BenoitLamarsaude <p>Thanks for this interesting article.</p> <p>At point 2, did must we find p = 0,4% for 4 accident on a 4 month period?</p> <p>Regards</p> <p>Thanks for this interesting article.</p> <p>At point 2, did must we find p = 0,4% for 4 accident on a 4 month period?</p> <p>Regards</p> Hmm.... I am a bit out of pra… tag:www.datasciencecentral.com,2014-08-12:6448529:Comment:193618 2014-08-12T09:31:43.406Z Alexander Kashko https://www.datasciencecentral.com/profile/AlexanderKashko <p>Hmm.... I am a bit out of practice with full mathematical rigor (mortis?) but here are my thoughts</p> <p>Assume the probabilty of a binary event happenning per unit time is p. The probability of it not happening is q = 1-p</p> <p>Assume p is small (say 0.01) then q is high. This means for any value of N the probability of an empty sequence (i.e the event not happening) is q**N and much higher than the probability of  a full sequence of length N. </p> <p>As a result if   a realisation of…</p> <p>Hmm.... I am a bit out of practice with full mathematical rigor (mortis?) but here are my thoughts</p> <p>Assume the probabilty of a binary event happenning per unit time is p. The probability of it not happening is q = 1-p</p> <p>Assume p is small (say 0.01) then q is high. This means for any value of N the probability of an empty sequence (i.e the event not happening) is q**N and much higher than the probability of  a full sequence of length N. </p> <p>As a result if   a realisation of this process is drawn out as a linear graph it would be dominatd by  large empty spaces and smaller spaces in which something would be happening.  It would look as if events were happening in clusters, even though they are random and a naive analysis would assume there was an underlying cause. </p> <p>The interesting case is where p=q = 0;5 in which case  I think it would look like an even distribution and be statistically symmetric  between did and did not happen</p> <p>As to air crashes I heard that 40% of all air journeys  involve near misses. Clearly this means a crash now and then is inevitable. It is amazing that  mid air collisions do not happen very often</p> <p><br/>I understand this is known as the inspector paradox.  I read that is applies ot the fact that busses may depart from a stop with an average ten minute gap but  you always seem to have a long wait. This is because the  arrival times are dominated by long waits. If you arrive randomly then you are likely to be in the middle of a long gap. </p> <p>It would seem that the way to detect this, if theprobabilities are unknown, would be to look at the distribution of intervals between the events ( e.g bus arrivals).  </p> <p>Now to get back to work while thinking about the full analysis, which isprobably on Wikipedia somewhere if I get  the right search term.</p> <p></p>