Comments - The law of series: why 4 plane crashing in 6 months is a coincidence - Data Science Central2020-11-25T11:56:44Zhttps://www.datasciencecentral.com/profiles/comment/feed?attachedTo=6448529%3ABlogPost%3A189743&xn_auth=noThanks for this interesting a…tag:www.datasciencecentral.com,2016-03-19:6448529:Comment:4030182016-03-19T18:58:42.569ZBenoit Lamarsaudehttps://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:1936182014-08-12T09:31:43.406ZAlexander Kashkohttps://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>
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