![]() X<-((accident_rate*1)^(all_data_counties $accidents)*exp(-accident_rate*1))/factorial(all_data_counties$accidents) But I'm aiming for the most simplest framework.Īssuming that the total accidents in Alabama are 1000, shouldn't Baldwin have a higher probability of an accident occurring, but the calculation says otherwise? accident_rate <- (merged_counties $accidents*merged_counties$average_miles)/merged_counties$total_miles What alternative model would better capture the idea of the probability of a car-accident? I understand that more variables must be considered like weather, types of road, the persons psychology at the time etc. ![]() States counties average_miles accidents total_miles TRAV_SP Which tells me that places with lower accidents have a higher probability of an accident occurring than places with more accidents, though I disagree. The problem I have with using the poisson distribution is that higher accidents are under-represented relative to smaller accidents. $t$ is the time, in this instance I'm working with data over 8 years so $t = 1, 2, 3, 4, 5, 6, 7,8$ $r$ is the accident rates which is calculated by the number of car-crashes within counties multiplied by the average miles traveled, and all of it divided by the total miles traveled of all vehicles in the county. My initial approach was to include a poisson distribution following these variables as parameters: Number of car-crashes within the Counties.This is a theoretical problem that I'm trying to calculate whilst at work.Įssentially, what is the probability of a car accident in a state given that these variables are provided to you:
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