Talk:Poisson distribution

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Waiting time to next event.[edit]

In the waiting time to the next event

P(T>t)=P(N_t=0)=e^{-\lambda t}.\,

This looks like it isn't normarmalized. since there should be a \lambda out in front. Am I wrong? Pdbailey 03:47, 11 Jan 2005 (UTC)

Yes; you're wrong. The normalizing constant should appear in the probability density function, but not in this expression, which is 1 minus the cumulative distribution function. Michael Hardy 03:50, 11 Jan 2005 (UTC)

Erlang Distribution[edit]

There's a refrence to erlang distribution, but the article does not mention the mutual dependence between Erlang Distribution and Poission Distribution. That is, the number of occurrences within a given interval follows a Poission distribution iff the time between occurrences follows an exponential distribution. (unsigned by user:Oobyduby)


Floor Functions in Summary Box[edit]

Since k is defined only over the set of natural numbers, the floor function of k or k+1 would never change the value. Should usage of and reference to floor functions in the function definitions in the summary box not be removed? — Preceding unsigned comment added by Antifrag (talkcontribs) 12:05, 14 December 2015 (UTC)

As written there, "The CDF is discontinuous at the integers of k and flat everywhere else because a variable that is Poisson distributed takes on only integer values." That is, the article follows the general definition of the CDF (for arbitrary distributions). For its restriction to natural numbers, of course, the floor function would not be needed. Boris Tsirelson (talk) 13:17, 14 December 2015 (UTC)