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Tj Poisson's birth name is Jillian Jayne Poisson.

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How can the Poisson distribution be applied to a continuous frequency distribution?

Let L(t) be the instantaneous average rate of occurrences per unit time, at time t. So, for the ordinary Poisson distribution with parameter L, we just have L(t)=L for all t.Let I be the integral of L(t) dt over a certain time interval [0,T], say.Then, assuming that L(t) is continuous, or maybe just Riemann integrable, the total number of occurrences during [0,T] simply follows a Poisson distribution with parameter I. This is the simple answer one might expect.To prove this (SKETCH: further estimates are needed to make this really rigorous): divide [0,T] into many small intervals [tj, tj+1). In each interval, the number of occurrences is approximately Poisson with parameter L(tj)(tj+1-tj).The occurrences in each small interval are all independent of each other; hence the total number in [0,T], which is the sum of all these, follows a Poisson distribution with parameter the sum of L(tj)(tj+1-tj).As you make the maximum size of the intervals shrink to zero, this sum tends towards I, the Riemann integral of L(t)dt over [0,T], as required.


What is tj oshie's real name?

Tj stands for Timothy James