http://www.mapleprimes.com/questions/121211-How-Can-We-Get-Mean-Value-Of-Time-Between en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Wed, 10 Jun 2026 21:34:30 GMT Wed, 10 Jun 2026 21:34:30 GMT The latest answers and comments added to the Question, How can we get mean value of time between arrival from mean of number of request? http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/questions/121211-How-Can-We-Get-Mean-Value-Of-Time-Between http://www.mapleprimes.com/questions/121211-How-Can-We-Get-Mean-Value-Of-Time-Between?ref=Feed:MaplePrimes:How can we get mean value of time between arrival from mean of number of request?:Comments#answer121213 <p>If I've understood your question correctly, I think the relation you cite applies only to a Poisson process. If events occur according to a Poisson process with parameter m, then the number of events in a period has a Poisson distribution with mean m, and the time between events has a exponential distribution with mean 1/m . &nbsp;This is not true when the underlying dstribution is not Poisson.</p> <p>If I've understood your question correctly, I think the relation you cite applies only to a Poisson process. If events occur according to a Poisson process with parameter m, then the number of events in a period has a Poisson distribution with mean m, and the time between events has a exponential distribution with mean 1/m . &nbsp;This is not true when the underlying dstribution is not Poisson.</p> 121213 Tue, 07 Jun 2011 17:28:04 Z longrob longrob http://www.mapleprimes.com/questions/121211-How-Can-We-Get-Mean-Value-Of-Time-Between?ref=Feed:MaplePrimes:How can we get mean value of time between arrival from mean of number of request?:Comments#answer123223 <p>Not rigorous, but assume we start at t=0 and n events occur at t1, t2, ..., tn The mean arrival rate is, I believe, n/tn.</p> <p>The mean inter-arrival time is 1/n*(t1-0 + t2-t1 + t3-t2 + ... + tn-t(n-1)) = 1/n*tn.&nbsp; There may have been some fudging with the end points, but you get the idea</p> <p>Not rigorous, but assume we start at t=0 and n events occur at t1, t2, ..., tn The mean arrival rate is, I believe, n/tn.</p> <p>The mean inter-arrival time is 1/n*(t1-0 + t2-t1 + t3-t2 + ... + tn-t(n-1)) = 1/n*tn.&nbsp; There may have been some fudging with the end points, but you get the idea</p> 123223 Fri, 24 Jun 2011 23:56:56 Z Joe Riel Joe Riel http://www.mapleprimes.com/questions/121211-How-Can-We-Get-Mean-Value-Of-Time-Between?ref=Feed:MaplePrimes:How can we get mean value of time between arrival from mean of number of request?:Comments#answer123272 <p>Assuming that you have a renewal process, this is the Elementary Renewal Theorem.&nbsp; See e.g. <a href="http://en.wikipedia.org/wiki/Renewal_theory">http://en.wikipedia.org/wiki/Renewal_theory</a> or look up Renewal Theory in a probability text, e.g. <a href="http://books.google.ca/books?id=0yDAZf1TfJEC">Ross, "Introduction to Probability Models"</a></p> <p>Assuming that you have a renewal process, this is the Elementary Renewal Theorem.&nbsp; See e.g. <a href="http://en.wikipedia.org/wiki/Renewal_theory">http://en.wikipedia.org/wiki/Renewal_theory</a> or look up Renewal Theory in a probability text, e.g. <a href="http://books.google.ca/books?id=0yDAZf1TfJEC">Ross, "Introduction to Probability Models"</a></p> 123272 Sun, 26 Jun 2011 17:16:32 Z Robert Israel Robert Israel