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What is intensity in Poisson (?)

1

$begingroup$

I am reading Stoikov's slides (slide 15), and there is a statement like this:

Number of stocks bought $N_t^b$ is Poisson with intensity $lambda^b
(p^b -s)$.

Does this mean that:

$$mathbb{P}[N_t^b = n] = frac{(lambda^b (p^b -s))^n}{n!} exp^{-(lambda^b (p^b -s))}$$

?

probability

share|cite|improve this question

asked Mar 22 at 21:44

i squared - Keep it Reali squared - Keep it Real

1,63211128

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Presumably, yes.
  $endgroup$
  – Math1000
  Mar 22 at 21:46
  

  
  
  
  

add a comment | 

1

$begingroup$

I am reading Stoikov's slides (slide 15), and there is a statement like this:

Number of stocks bought $N_t^b$ is Poisson with intensity $lambda^b
(p^b -s)$.

Does this mean that:

$$mathbb{P}[N_t^b = n] = frac{(lambda^b (p^b -s))^n}{n!} exp^{-(lambda^b (p^b -s))}$$

?

probability

share|cite|improve this question

asked Mar 22 at 21:44

i squared - Keep it Reali squared - Keep it Real

1,63211128

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Presumably, yes.
  $endgroup$
  – Math1000
  Mar 22 at 21:46
  

  
  
  
  

add a comment | 

$begingroup$

I am reading Stoikov's slides (slide 15), and there is a statement like this:

Number of stocks bought $N_t^b$ is Poisson with intensity $lambda^b
(p^b -s)$.

Does this mean that:

$$mathbb{P}[N_t^b = n] = frac{(lambda^b (p^b -s))^n}{n!} exp^{-(lambda^b (p^b -s))}$$

?

probability

share|cite|improve this question

asked Mar 22 at 21:44

i squared - Keep it Reali squared - Keep it Real

1,63211128

$endgroup$

share|cite|improve this question

asked Mar 22 at 21:44

i squared - Keep it Reali squared - Keep it Real

1,63211128

share|cite|improve this question

asked Mar 22 at 21:44

i squared - Keep it Reali squared - Keep it Real

1,63211128

asked Mar 22 at 21:44

i squared - Keep it Reali squared - Keep it Real

1,63211128

asked Mar 22 at 21:44

i squared - Keep it Reali squared - Keep it Real

1,63211128

1 Answer
1

active

oldest

votes

1

$begingroup$

The "intensity" $lambda^b
(p^b -s)$ is just the average number of events in a time interval.

The term "intensity" is used to indicate "how strong" is the Poisson process under investigation, i.e., the higher is the average number of events in time interval, the stronger (i.e. the "more intense") is the process.

share|cite|improve this answer

edited Mar 22 at 22:22

answered Mar 22 at 21:47

the_candymanthe_candyman

9,14032147

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you. I was also wondering whether there should be any dependence on time in my equation
  $endgroup$
  – i squared - Keep it Real
  Mar 22 at 22:02
  

  
  
  
  

add a comment | 

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1

$begingroup$

The "intensity" $lambda^b
(p^b -s)$ is just the average number of events in a time interval.

The term "intensity" is used to indicate "how strong" is the Poisson process under investigation, i.e., the higher is the average number of events in time interval, the stronger (i.e. the "more intense") is the process.

share|cite|improve this answer

edited Mar 22 at 22:22

answered Mar 22 at 21:47

the_candymanthe_candyman

9,14032147

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you. I was also wondering whether there should be any dependence on time in my equation
  $endgroup$
  – i squared - Keep it Real
  Mar 22 at 22:02
  

  
  
  
  

add a comment | 

1

$begingroup$

The "intensity" $lambda^b
(p^b -s)$ is just the average number of events in a time interval.

The term "intensity" is used to indicate "how strong" is the Poisson process under investigation, i.e., the higher is the average number of events in time interval, the stronger (i.e. the "more intense") is the process.

share|cite|improve this answer

edited Mar 22 at 22:22

answered Mar 22 at 21:47

the_candymanthe_candyman

9,14032147

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you. I was also wondering whether there should be any dependence on time in my equation
  $endgroup$
  – i squared - Keep it Real
  Mar 22 at 22:02
  

  
  
  
  

add a comment | 

$begingroup$

The "intensity" $lambda^b
(p^b -s)$ is just the average number of events in a time interval.

The term "intensity" is used to indicate "how strong" is the Poisson process under investigation, i.e., the higher is the average number of events in time interval, the stronger (i.e. the "more intense") is the process.

share|cite|improve this answer

edited Mar 22 at 22:22

answered Mar 22 at 21:47

the_candymanthe_candyman

9,14032147

$endgroup$

share|cite|improve this answer

edited Mar 22 at 22:22

answered Mar 22 at 21:47

the_candymanthe_candyman

9,14032147

answered Mar 22 at 21:47

the_candymanthe_candyman

9,14032147

answered Mar 22 at 21:47

the_candymanthe_candyman

9,14032147