For the Poisson Distribution a. Is λ×T a parameter of position, scale, shape or a combination?...

For the Poisson Distribution

a. Is λ×T a parameter of position, scale, shape or a combination? Explain.

b. We can treat “λ×T” as a single parameter, but they actually represent two parameters: λ and T. Say you stand by the side of the road and count the number of cars that pass by you in one minute. After repeating this process 10 times you find the average number of cars that pass in 10 minutes. In this case, what is λ and what is T?

Expert Solution

a.Poisson was a French mathematician, and amongst the many contributions he made, proposed the Poisson distribution, with the example of modelling the number of soldiers accidentally injured or killed from kicks by horses. This distribution became useful as it models events, particularly uncommon events.

Counts of events, based on the Poisson distribution, is a frequently encountered model in medical research. Examples of this are number of falls, asthma attacks, number of cells, and so on. The Poisson parameter Lambda (λ) is the total number of events (k) divided by the number of units (T) in the data (λ = k/T). The unit forms the basis or denominator for calculation of the average, and need not be individual cases or research subjects. For example, the number of asthma attacks may be based on the number of child months, or the number of pregnancies based on the number of women years in using a particular contraceptive

So, λ×T a parameter of combination

b. λ is average number of cars that pass in 10 minutes

T is 10 times

orchestra answered 1 year ago

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