3 ms·

Worth mentioning is the The Waiting Time Paradox: "When waiting for a bus that comes on average every 10 minutes, your average waiting time will be 10 minutes.

by air7 7y ago

Worth mentioning is the The Waiting Time Paradox: "When waiting for a bus that comes on average every 10 minutes, your average waiting time will be 10 minutes." And worse "when the average span between arrivals is N minutes, the average span experienced by riders is 2N minutes." These realizations about Poisson distributions have a lot of real-world implications such as packet traffic, call center calls, etc. - https://jakevdp.github.io/blog/2018/09/13/waiting-time-paradox/ https://jakevdp.github.io/blog/2018/09/13/waiting-time-parad...

billforsternz 7y ago
For some reason this is the post that took me back to a EE numeric analysis and stats practical exercise nearly 40 years ago. A friend encounters a miserable looking me standing on the street with a clipboard and a stopwatch. Friend: "What the hell are you doing?". Me: "Testing the hypothesis that passing traffic is Poisson distributed".
lukaszsamson 7y ago
This also applies to bitcoin blocks
rrss 7y ago
I'll quote from the conclusion of that article, because the frequent assumptions that bus arrivals are a poisson process peeve me and this article did a good job of actually testing that assumption: > Even without a statistical test, it's clear by eye that the actual arrival intervals are definitely not exponentially distributed, which is the basic assumption on which the waiting time paradox rests. > The average waiting times are are perhaps a minute or two longer than half the scheduled interval, but not equal to the scheduled interval as the waiting time paradox implied. In other words, the inspection paradox is confirmed, but the waiting time paradox does not appear to match reality. > the above analysis shows pretty definitively that the core assumption behind the waiting time paradox — that the arrival of buses follows the statistics of a Poisson process — is not well-founded.

by air7 7y ago

billforsternz 7y ago

For some reason this is the post that took me back to a EE numeric analysis and stats practical exercise nearly 40 years ago. A friend encounters a miserable looking me standing on the street with a clipboard and a stopwatch. Friend: "What the hell are you doing?". Me: "Testing the hypothesis that passing traffic is Poisson distributed".

lukaszsamson 7y ago

This also applies to bitcoin blocks

rrss 7y ago

I'll quote from the conclusion of that article, because the frequent assumptions that bus arrivals are a poisson process peeve me and this article did a good job of actually testing that assumption: > Even without a statistical test, it's clear by eye that the actual arrival intervals are definitely not exponentially distributed, which is the basic assumption on which the waiting time paradox rests. > The average waiting times are are perhaps a minute or two longer than half the scheduled interval, but not equal to the scheduled interval as the waiting time paradox implied. In other words, the inspection paradox is confirmed, but the waiting time paradox does not appear to match reality. > the above analysis shows pretty definitively that the core assumption behind the waiting time paradox — that the arrival of buses follows the statistics of a Poisson process — is not well-founded.