Poisson process VS poisson law : what is the subtlety?
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I always heard that for rare event we always use Poisson process. Example : We know that at each minute, when have a mean of $3$ call. Therefore, $X$ is a poisson process, and if $X$ denote the number of call, then $$mathbb P{X=k}=e^{-3}frac{3^k}{k!}.$$
But now, in my course today, to stud rare event we used Poisson process. What is this new tool, I don't understand where to use it ? Could someone explain by example ?
Law for rare event By poisson distribution
Law for rare event By poisson process
probability
asked Jan 18 at 19:07
NewMathNewMath
4059
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add a comment |
$begingroup$
I always heard that for rare event we always use Poisson process. Example : We know that at each minute, when have a mean of $3$ call. Therefore, $X$ is a poisson process, and if $X$ denote the number of call, then $$mathbb P{X=k}=e^{-3}frac{3^k}{k!}.$$
But now, in my course today, to stud rare event we used Poisson process. What is this new tool, I don't understand where to use it ? Could someone explain by example ?
Law for rare event By poisson distribution
Law for rare event By poisson process
probability
asked Jan 18 at 19:07
NewMathNewMath
4059
$endgroup$
$begingroup$
Please clarify the distinction you are trying to make. A Poisson process is a random process which has a Poisson distribution.
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– herb steinberg
Jan 18 at 20:45
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I have the impression that both work for rare event : @herbsteinberg
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– NewMath
Jan 18 at 21:33
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Basically they are describing the same thing. The Poisson process is a term used for random variables, while a Poisson distribution is the term describing its distribution. For example: Let $X$ be the number of counts per minute of some process where the mean number of counts is $a$, the the density function $P(X=n)=e^{-a}frac{a^n}{n!}$. The distribution function $P(Xle n)=e^{-a}sum_{k=0}^nfrac{a^k}{k!}$. It doesn't have to be a rare event. It is used for discrete events where there is no theoretical upper limit.
$endgroup$
– herb steinberg
Jan 18 at 23:01
add a comment |
$begingroup$
I always heard that for rare event we always use Poisson process. Example : We know that at each minute, when have a mean of $3$ call. Therefore, $X$ is a poisson process, and if $X$ denote the number of call, then $$mathbb P{X=k}=e^{-3}frac{3^k}{k!}.$$
But now, in my course today, to stud rare event we used Poisson process. What is this new tool, I don't understand where to use it ? Could someone explain by example ?
Law for rare event By poisson distribution
Law for rare event By poisson process
probability
asked Jan 18 at 19:07
NewMathNewMath
4059
$endgroup$
I always heard that for rare event we always use Poisson process. Example : We know that at each minute, when have a mean of $3$ call. Therefore, $X$ is a poisson process, and if $X$ denote the number of call, then $$mathbb P{X=k}=e^{-3}frac{3^k}{k!}.$$
But now, in my course today, to stud rare event we used Poisson process. What is this new tool, I don't understand where to use it ? Could someone explain by example ?
Law for rare event By poisson distribution
Law for rare event By poisson process
probability
probability
asked Jan 18 at 19:07
NewMathNewMath
4059
asked Jan 18 at 19:07
NewMathNewMath
4059
asked Jan 18 at 19:07
NewMathNewMath
4059
asked Jan 18 at 19:07
NewMathNewMath
4059
asked Jan 18 at 19:07
NewMathNewMath
4059
4059
$begingroup$
Please clarify the distinction you are trying to make. A Poisson process is a random process which has a Poisson distribution.
$endgroup$
– herb steinberg
Jan 18 at 20:45
$begingroup$
I have the impression that both work for rare event : @herbsteinberg
$endgroup$
– NewMath
Jan 18 at 21:33
$begingroup$
Basically they are describing the same thing. The Poisson process is a term used for random variables, while a Poisson distribution is the term describing its distribution. For example: Let $X$ be the number of counts per minute of some process where the mean number of counts is $a$, the the density function $P(X=n)=e^{-a}frac{a^n}{n!}$. The distribution function $P(Xle n)=e^{-a}sum_{k=0}^nfrac{a^k}{k!}$. It doesn't have to be a rare event. It is used for discrete events where there is no theoretical upper limit.
$endgroup$
– herb steinberg
Jan 18 at 23:01
add a comment |
$begingroup$
Please clarify the distinction you are trying to make. A Poisson process is a random process which has a Poisson distribution.
$endgroup$
– herb steinberg
Jan 18 at 20:45
$begingroup$
I have the impression that both work for rare event : @herbsteinberg
$endgroup$
– NewMath
Jan 18 at 21:33
$begingroup$
Basically they are describing the same thing. The Poisson process is a term used for random variables, while a Poisson distribution is the term describing its distribution. For example: Let $X$ be the number of counts per minute of some process where the mean number of counts is $a$, the the density function $P(X=n)=e^{-a}frac{a^n}{n!}$. The distribution function $P(Xle n)=e^{-a}sum_{k=0}^nfrac{a^k}{k!}$. It doesn't have to be a rare event. It is used for discrete events where there is no theoretical upper limit.
$endgroup$
– herb steinberg
Jan 18 at 23:01
$begingroup$
Please clarify the distinction you are trying to make. A Poisson process is a random process which has a Poisson distribution.
$endgroup$
– herb steinberg
Jan 18 at 20:45
$begingroup$
Please clarify the distinction you are trying to make. A Poisson process is a random process which has a Poisson distribution.
$endgroup$
– herb steinberg
Jan 18 at 20:45
$begingroup$
I have the impression that both work for rare event : @herbsteinberg
$endgroup$
– NewMath
Jan 18 at 21:33
$begingroup$
I have the impression that both work for rare event : @herbsteinberg
$endgroup$
– NewMath
Jan 18 at 21:33
$begingroup$
Basically they are describing the same thing. The Poisson process is a term used for random variables, while a Poisson distribution is the term describing its distribution. For example: Let $X$ be the number of counts per minute of some process where the mean number of counts is $a$, the the density function $P(X=n)=e^{-a}frac{a^n}{n!}$. The distribution function $P(Xle n)=e^{-a}sum_{k=0}^nfrac{a^k}{k!}$. It doesn't have to be a rare event. It is used for discrete events where there is no theoretical upper limit.
$endgroup$
– herb steinberg
Jan 18 at 23:01
$begingroup$
Basically they are describing the same thing. The Poisson process is a term used for random variables, while a Poisson distribution is the term describing its distribution. For example: Let $X$ be the number of counts per minute of some process where the mean number of counts is $a$, the the density function $P(X=n)=e^{-a}frac{a^n}{n!}$. The distribution function $P(Xle n)=e^{-a}sum_{k=0}^nfrac{a^k}{k!}$. It doesn't have to be a rare event. It is used for discrete events where there is no theoretical upper limit.
$endgroup$
– herb steinberg
Jan 18 at 23:01
add a comment |
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$begingroup$
Please clarify the distinction you are trying to make. A Poisson process is a random process which has a Poisson distribution.
$endgroup$
– herb steinberg
Jan 18 at 20:45
$begingroup$
I have the impression that both work for rare event : @herbsteinberg
$endgroup$
– NewMath
Jan 18 at 21:33
$begingroup$
Basically they are describing the same thing. The Poisson process is a term used for random variables, while a Poisson distribution is the term describing its distribution. For example: Let $X$ be the number of counts per minute of some process where the mean number of counts is $a$, the the density function $P(X=n)=e^{-a}frac{a^n}{n!}$. The distribution function $P(Xle n)=e^{-a}sum_{k=0}^nfrac{a^k}{k!}$. It doesn't have to be a rare event. It is used for discrete events where there is no theoretical upper limit.
$endgroup$
– herb steinberg
Jan 18 at 23:01