What does "fit a poisson distribution" mean?

My question is:

"Fit a Poisson distribution to the following frequency distribution and test the goodness of ft. State clearly the hypothesis being tested and the conclusion which is reached".

After looking online, I found out the hypothesis would simply be H(o) - The following data fit's a Poisson distrubution, and H(1) - The data doesn't.

I think that is correct as the question is all the data we have been given.

However I don't understand what is meant by "Fit a Poisson distribution" and when testing the goodness of fit, how would I work out the expected values as our table as 2 rows, one for 'x' and one for the frequency, and again, the question is the whole question we have been given, there are no other parts to it.

Thank you :smile:

Reply 1

CookieGhoul

14

Right. That is correct that the null hypothesis is that the variable and the data fits a Poisson distribution. To calucate the expected values, you just calcuate the probability of the event (eg : P(x=2)) and you multiply that by the total observed frequencies. You know then you have to find the {(Observed frequency - Expected frequency)^2}/{Expected frequency}, to caluclate the Chi-squared value

Reply 2

claret_n_blue

OP

17

Original post by CookieGhoul

Right. That is correct that the null hypothesis is that the variable and the data fits a Poisson distribution. To calucate the expected values, you just calcuate the probability of the event (eg : P(x=2)) and you multiply that by the total observed frequencies. You know then you have to find the {(Observed frequency - Expected frequency)^2}/{Expected frequency}, to caluclate the Chi-squared value

Then when I do this chi squared bit, what am I looking for?

Reply 3

CookieGhoul

14

Nothing. Just compare it with the value in the formula booklet with the appropriate level of significance. I assume that you know how to do this ?

Reply 4

claret_n_blue

OP

17

Original post by CookieGhoul

Nothing. Just compare it with the value in the formula booklet with the appropriate level of significance. I assume that you know how to do this ?

Oh and do a normal hypotheses test thing with it? Cool, thanks :smile:

Just one more question, my very first one lol. What does "fit a poission distribution" mean? Is it simply drawing the Poisson distribution?

Reply 5

CookieGhoul

14

Original post by claret_n_blue

Oh and do a normal hypotheses test thing with it? Cool, thanks :smile:

Just one more question, my very first one lol. What does "fit a poission distribution" mean? Is it simply drawing the Poisson distribution?

Lol no. Your not drawing it. When they say "fit", they mean whether or not the data corresponds to a variable that follows a poisson distribution. Your expected values are then calulated using the probability formulas for the Poisson distribution

Reply 6

claret_n_blue

OP

17

Original post by CookieGhoul

Lol no. Your not drawing it. When they say "fit", they mean whether or not the data corresponds to a variable that follows a poisson distribution. Your expected values are then calulated using the probability formulas for the Poisson distribution

So the whole point of them mentioning Poission is to tell me what formula/tables I have to use to work out the expected values. If they said fit a Binomial, would I do the same thing but using the binomial formula instead?

Reply 7

CookieGhoul

14

Original post by claret_n_blue

So the whole point of them mentioning Poission is to tell me what formula/tables I have to use to work out the expected values. If they said fit a Binomial, would I do the same thing but using the binomial formula instead?

Exactly

What does "fit a poisson distribution" mean?

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