Birth immigration process
$begingroup$
I'm having some problem with this question.
A model for the distribution of the number of goals scored in soccer matches suggests that if n goals have already been scored by time t, then the probability of another goal being scored in the next time interval (t, t+$delta$t) is (v+$lambda$n)$delta$t +o($delta$t), where the time scale is measured in minutes. Show that this leads to a negative binomial distribution for the numbers of goals per match. (Assume that the effective duration of a game is 90 minutes - any added time is supposed to make up exactly for stoppages due to injury or substitutions.)
I understand that this is a birth-immigration process and I can show that that the a pure birth process is a negative binomial distribution but I can't figure out how to incorporate the immigration process.Any help would be appreciated.
probability stochastic-processes
asked Nov 22 '14 at 22:44
ElliotElliot
91
$endgroup$
add a comment |
$begingroup$
I'm having some problem with this question.
A model for the distribution of the number of goals scored in soccer matches suggests that if n goals have already been scored by time t, then the probability of another goal being scored in the next time interval (t, t+$delta$t) is (v+$lambda$n)$delta$t +o($delta$t), where the time scale is measured in minutes. Show that this leads to a negative binomial distribution for the numbers of goals per match. (Assume that the effective duration of a game is 90 minutes - any added time is supposed to make up exactly for stoppages due to injury or substitutions.)
I understand that this is a birth-immigration process and I can show that that the a pure birth process is a negative binomial distribution but I can't figure out how to incorporate the immigration process.Any help would be appreciated.
probability stochastic-processes
asked Nov 22 '14 at 22:44
ElliotElliot
91
$endgroup$
1
$begingroup$
"I understand that this is a birth-immigration process" Hmmm... no. At most a birth process (which brings not much useful to solve the question).
$endgroup$
– Did
Jan 14 at 11:54
add a comment |
$begingroup$
I'm having some problem with this question.
A model for the distribution of the number of goals scored in soccer matches suggests that if n goals have already been scored by time t, then the probability of another goal being scored in the next time interval (t, t+$delta$t) is (v+$lambda$n)$delta$t +o($delta$t), where the time scale is measured in minutes. Show that this leads to a negative binomial distribution for the numbers of goals per match. (Assume that the effective duration of a game is 90 minutes - any added time is supposed to make up exactly for stoppages due to injury or substitutions.)
I understand that this is a birth-immigration process and I can show that that the a pure birth process is a negative binomial distribution but I can't figure out how to incorporate the immigration process.Any help would be appreciated.
probability stochastic-processes
asked Nov 22 '14 at 22:44
ElliotElliot
91
$endgroup$
I'm having some problem with this question.
A model for the distribution of the number of goals scored in soccer matches suggests that if n goals have already been scored by time t, then the probability of another goal being scored in the next time interval (t, t+$delta$t) is (v+$lambda$n)$delta$t +o($delta$t), where the time scale is measured in minutes. Show that this leads to a negative binomial distribution for the numbers of goals per match. (Assume that the effective duration of a game is 90 minutes - any added time is supposed to make up exactly for stoppages due to injury or substitutions.)
I understand that this is a birth-immigration process and I can show that that the a pure birth process is a negative binomial distribution but I can't figure out how to incorporate the immigration process.Any help would be appreciated.
probability stochastic-processes
probability stochastic-processes
asked Nov 22 '14 at 22:44
ElliotElliot
91
asked Nov 22 '14 at 22:44
ElliotElliot
91
asked Nov 22 '14 at 22:44
ElliotElliot
91
asked Nov 22 '14 at 22:44
ElliotElliot
91
asked Nov 22 '14 at 22:44
ElliotElliot
91
91
1
$begingroup$
"I understand that this is a birth-immigration process" Hmmm... no. At most a birth process (which brings not much useful to solve the question).
$endgroup$
– Did
Jan 14 at 11:54
add a comment |
1
$begingroup$
"I understand that this is a birth-immigration process" Hmmm... no. At most a birth process (which brings not much useful to solve the question).
$endgroup$
– Did
Jan 14 at 11:54
1
1
$begingroup$
"I understand that this is a birth-immigration process" Hmmm... no. At most a birth process (which brings not much useful to solve the question).
$endgroup$
– Did
Jan 14 at 11:54
$begingroup$
"I understand that this is a birth-immigration process" Hmmm... no. At most a birth process (which brings not much useful to solve the question).
$endgroup$
– Did
Jan 14 at 11:54
add a comment |
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$begingroup$
"I understand that this is a birth-immigration process" Hmmm... no. At most a birth process (which brings not much useful to solve the question).
$endgroup$
– Did
Jan 14 at 11:54