To properly apply a Poisson distribution to model SIDS deaths following vaccinations one would need more than just the number of SIDS deaths and the vaccination schedule. Specifically, you would also need: The total number of babies vaccinated over the analysis time period. This is because the key Poisson parameter λ represents the avera…
To properly apply a Poisson distribution to model SIDS deaths following vaccinations one would need more than just the number of SIDS deaths and the vaccination schedule. Specifically, you would also need: The total number of babies vaccinated over the analysis time period. This is because the key Poisson parameter λ represents the average rate of SIDS deaths per vaccinated baby over a given time window following vaccination. Without knowing the total number vaccinated, you can't accurately calculate λ, the SIDS rate per vaccinated baby. Simply assuming λ based on the vaccination schedule alone is invalid. Without the full underlying dataset, any Poisson model will be based on unfounded assumptions. The stated 1/30 probability of SIDS within 48 hours of vaccination is purely hypothetical, not derived from actual data. The Poisson distribution models the probability of observing X events in an interval given a known average rate of events (λ). Without empirical data on the actual rate of SIDS occurrences within a time window of vaccinations, λ is unknown. Plugging in an assumed probability like 1/30 as λ gives an invalid model - since this doesn't represent the true observed rate. Any probabilities or conclusions derived from this assumed Poisson distribution are therefore statistically unfounded.
To properly apply a Poisson distribution to model SIDS deaths following vaccinations one would need more than just the number of SIDS deaths and the vaccination schedule. Specifically, you would also need: The total number of babies vaccinated over the analysis time period. This is because the key Poisson parameter λ represents the average rate of SIDS deaths per vaccinated baby over a given time window following vaccination. Without knowing the total number vaccinated, you can't accurately calculate λ, the SIDS rate per vaccinated baby. Simply assuming λ based on the vaccination schedule alone is invalid. Without the full underlying dataset, any Poisson model will be based on unfounded assumptions. The stated 1/30 probability of SIDS within 48 hours of vaccination is purely hypothetical, not derived from actual data. The Poisson distribution models the probability of observing X events in an interval given a known average rate of events (λ). Without empirical data on the actual rate of SIDS occurrences within a time window of vaccinations, λ is unknown. Plugging in an assumed probability like 1/30 as λ gives an invalid model - since this doesn't represent the true observed rate. Any probabilities or conclusions derived from this assumed Poisson distribution are therefore statistically unfounded.
Good luck getting study funded!