- #1
Rampart
- 27
- 0
Hey guys, what's up? I have some questions regarding the Poisson Process. I checked some threads, but not all, so forgive me if these questions have been answered before.
1)Lets say I am given some some tables or/and graphs or generally speaking some data and I am asked to find out if the Poisson model can describe it. What exactly should I look for?
Should I focus on these 2?
a)Should I prove the Poisson distribution
.
?
b)Should I prove that it has independent increments?
2)If i want to show that Poisson Process isn't suitable, should I just show that mean!=variance or is this not enough?
3) As far as the parameter λ is concerned. Ιf It changes over time, then the Poisson Process in non-homogeneous and if it is a constant then it is homogeneous, right?
So If I have some data(events) in a year, in order to be homogeneous, the following equation must hold----->
(x units in t1)/t1=(z units in t2)/t2 ? And if with this logic, I find for 2 periods(lets assume that these periods are overlapping,just to see if there is a problem with that :P ) of time, λ= 800000 units/month and
λ'=800001 units/month then what? Are these considered equal even though they aren't, and if yes, how to know what difference isn't bad enough?
Thanks in advance for your time!
1)Lets say I am given some some tables or/and graphs or generally speaking some data and I am asked to find out if the Poisson model can describe it. What exactly should I look for?
Should I focus on these 2?
a)Should I prove the Poisson distribution
.
b)Should I prove that it has independent increments?
2)If i want to show that Poisson Process isn't suitable, should I just show that mean!=variance or is this not enough?
3) As far as the parameter λ is concerned. Ιf It changes over time, then the Poisson Process in non-homogeneous and if it is a constant then it is homogeneous, right?
So If I have some data(events) in a year, in order to be homogeneous, the following equation must hold----->
(x units in t1)/t1=(z units in t2)/t2 ? And if with this logic, I find for 2 periods(lets assume that these periods are overlapping,just to see if there is a problem with that :P ) of time, λ= 800000 units/month and
λ'=800001 units/month then what? Are these considered equal even though they aren't, and if yes, how to know what difference isn't bad enough?
Thanks in advance for your time!