Timeline for Can Negative Binomial parameters be treated like Poisson?
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| Sep 20, 2020 at 12:43 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Sep 20, 2020 at 12:25 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Sep 20, 2020 at 11:58 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Sep 20, 2020 at 6:42 | comment | added | Sextus Empiricus | @PedroSebe I mean, for number of events distributed by the Poisson distribution the corresponding waiting time for time between events is exponential distributed (or gamma distributed when you wait for the n-th event). For the binomial distribution you could see the waiting time as a geometric distributed variable. But what would be the corresponding waiting time distribution, if there is one, for a negative binomial distribution? | |
| Sep 20, 2020 at 2:49 | comment | added | PedroSebe | @SextusEmpiricus using a parameter r != 1 means the waiting time distribution is a Gamma instead of an Exponential. | |
| Sep 19, 2020 at 23:01 | comment | added | Sextus Empiricus | @J Doe , it will depend on the origin of the overdispersion. I guess that PedroSebe's answer is more typically found when you have a situation that the source of overdispersion is a waiting time that is not exponential distributed (although I am wondering what sort waiting time distribution corresponds to a negative binomial distribution for number of events and imagine that it is only approximately negative binomial distributed). The situation I used, where r parameter is constant, is when you consider a waiting time that is exponential distributed but the rate varies over a long timescale. | |
| Sep 19, 2020 at 20:22 | comment | added | J Doe | Thanks for this! I'm a little confused so I'm going to try and state it back to you. So say I fit NB(r_x, p_x) to a time series of counts (measuring frequency is every x=30 minutes), and then I have new data come in, its a count of events in the last y=45 minutes. I can determine the probability of that many events occurring in 45 minutes given the data is from a NB(r_x, p_x) distribution by calculating the PMF of NB(r_x, p_y), where p_y = 1 / ( (1/p_x - 1) * 30/45 + 1) )? And I don't need to scale the parameter r_x to adjust to time y=45 minutes? | |
| Sep 19, 2020 at 19:09 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Sep 19, 2020 at 18:53 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Sep 19, 2020 at 18:47 | history | answered | Sextus Empiricus | CC BY-SA 4.0 |