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Karen
May 6th 2005, 11:23 AM
I am unsure when to use integer correction. My study manual says to use integer correction if you are trying to find P[n<X<m] and X is discrete and integer valued.
So I thought that integer correction should be used on the following problem:

An insurance company issues 1250 vision care insurance policies. The number of claims filed by a policyholder under a vision care insurance policy during one year is a Poisson random variable with mean 2. Assume the numbers of claims filed by distinct policyholders are independent of one another. What is the approximate probability that there is a total of between 2450 and 2600 claims during a one-year period?

I did this problem using integer correction because I thought that it was supposed to be used.
Can someone explain why it should not be used in this case?
In what cases should integer correction be used?

Thanks a lot!

wat
May 6th 2005, 03:27 PM
I am unsure when to use integer correction. My study manual says to use integer correction if you are trying to find P[n<X<m] and X is discrete and integer valued.
So I thought that integer correction should be used on the following problem:

An insurance company issues 1250 vision care insurance policies. The number of claims filed by a policyholder under a vision care insurance policy during one year is a Poisson random variable with mean 2. Assume the numbers of claims filed by distinct policyholders are independent of one another. What is the approximate probability that there is a total of between 2450 and 2600 claims during a one-year period?

I did this problem using integer correction because I thought that it was supposed to be used.
Can someone explain why it should not be used in this case?
In what cases should integer correction be used?

Thanks a lot!

How did you use integer correction? Did you try P(2449.5 < X < 2600.5)?

Karen
May 6th 2005, 04:20 PM
Yeah, that is what I did for integer correction.
I still got the correct answer (I think because 2449.5 is not much different than 2450), but the answer key does the problem without integer correction.

When should integer correction be used?

Thanks

Act18
May 7th 2005, 06:01 PM
The actex manual says that it would generally be mentioned in the question if the integer correction is to be used.

krzysio
May 8th 2005, 11:55 AM
Most textbooks call it "continuity correction". It is a very intuitive concept once you draw the PDF of the discrete distribution you are approximating and the PDF of the normal distribution you are using for approximation -- then take a look at the two areas which show probabilities you are comparing. There will be half a "block" from the discrete distribution sticking out or in. Just try it. Once you understand this, you will no longer need some official rules for using it, it will just stare you in the face when it is needed. Try it and tell me what happened. Good luck.

Yours,
Krzys'

Karen
May 10th 2005, 09:30 AM
Most textbooks call it "continuity correction". It is a very intuitive concept once you draw the PDF of the discrete distribution you are approximating and the PDF of the normal distribution you are using for approximation -- then take a look at the two areas which show probabilities you are comparing. There will be half a "block" from the discrete distribution sticking out or in. Just try it. Once you understand this, you will no longer need some official rules for using it, it will just stare you in the face when it is needed. Try it and tell me what happened. Good luck.

Yours,
Krzys'


I drew the pdfs for the following problem: An insurer has a portfolio of 1000 independent one-year term insurance policies. For any one policy, there is a probability of 0.01 that there will be a claim. Find the approximate probability that the insurer will experience at least 15 claims.

I see that at 15, the pdf of the discrete distribution is inside the pdf of the normal distribution. Is this the half "block" that you referred to? But then after 20, the pdf of the discrete distribution is outside the pdf of the normal distribution. So at first I saw why we should use 14.5 instead of 15, but after looking at the distributions past 20, I am unsure. Do you have any further advice?

Thanks,
Karen

krzysio
May 13th 2005, 12:54 AM
At every integer value of the discrete random variable draw a rectangle centered at that integer at its base and of height equal to the probability assigned to that integer by the discrete distribution. Then draw the PDF of the corresponding normal distribution over the set of rectangles (or blocks, as I called them before). Then mark the probability you are loooking for on the discrete distribution and the continuous distribution. Do you see the difference of half a block between them?

Yours,
Krzys'

P.S. Always remember that the Central Limit Theorem, which you are using for this, says that sum of IID random variables can be approximated with a normal distribution with the same mean and variance as that sum. Do you know that? If not, well "you was robbed" (this is a quite from the greatest Goldie Hawn movie
"Wildcats", go rent that movie the night before the exam, and pay attention to
the scene about the hubcaps) in your probability class.



I drew the pdfs for the following problem: An insurer has a portfolio of 1000 independent one-year term insurance policies. For any one policy, there is a probability of 0.01 that there will be a claim. Find the approximate probability that the insurer will experience at least 15 claims.

I see that at 15, the pdf of the discrete distribution is inside the pdf of the normal distribution. Is this the half "block" that you referred to? But then after 20, the pdf of the discrete distribution is outside the pdf of the normal distribution. So at first I saw why we should use 14.5 instead of 15, but after looking at the distributions past 20, I am unsure. Do you have any further advice?

Thanks,
Karen

Alice2005
December 27th 2005, 10:42 AM
[QUOTE=krzysio]At every integer value of the discrete random variable draw a rectangle centered at that integer at its base and of height equal to the probability assigned to that integer by the discrete distribution.
QUOTE]

I think this webcite has a good demonstration...
http://www.cs.uni.edu/~campbell/stat/prob9.html


As far as I understand, Integer Correction should be used when Approximating a discrete random variable (like Binomial or Poisson) by using a continuous distribution (Normal). And when n is large, the integer correction doesn't matter.

Am I wrong?

krzysio
December 29th 2005, 11:28 PM
[QUOTE=krzysio]At every integer value of the discrete random variable draw a rectangle centered at that integer at its base and of height equal to the probability assigned to that integer by the discrete distribution.
QUOTE]

I think this webcite has a good demonstration...
http://www.cs.uni.edu/~campbell/stat/prob9.html
As far as I understand, Integer Correction should be used when Approximating a discrete random variable (like Binomial or Poisson) by using a continuous distribution (Normal). And when n is large, the integer correction doesn't matter.
Am I wrong?

You are most certainly right, that web site presents it nicely.
Good luck!
Yours,
Krzys'

Alice2005
December 30th 2005, 10:58 PM
Thanks for your help Krzys