1. ## Applied probability

Hello,
This is my inaugural post on this forum. Without giving my life story, I would like to say that I am in no way mathematically savvy and the highest level that I have "properly" studied mathematics is year 12 maths B. In saying that though I have a rather keen interest in mathematics and like to study it in my spare time.

I was wondering if someone who is actually good at maths could share their insight on the following (ill-defined)problem.

A company has employed the following number of people over the last 12 months (June hires, July hires, ........, April, May):

30, 40, 60, 20, 34, 61, 58, 42, 39, 56, 59, and 48. So obviously the total for the year is 547 and the average number of hires per month is roughly 45.48.

At the same time the number of firings over the last year is (June hires, July hires, ........, April, May):

43 ,62 , 23, 59, 50, 34, 48, 25, 43, 36, 25, 56. Again the total is 504 and the average firings per month is 42.

I was wondering if there was anyway that these figures could be used to predict the probability of how many hires and/or terminations would be made in 1 month's time, 2 months time, 12 months time, n months time?

When considering this I've come up with a few ideas based upon the things I know about probability distributions (which, albeit, is very little).

First of all I was thinking that for the number of people employed, a Poisson distribution could be used, where the lambda variable is the mean of all employment numbers at a monthly level because it is my understanding that a Poisson distribution tracks "movement in".

But then it crossed my mind that what if the number of hires were conditional on the number of terminations? Could some conditional probability be used?

But that begs the question, how could one determine if the hires and firings were either dependent or independent?

Also, if the hires did have a Poisson distribution, what sort of distribution could the terminations have? Is there something that could be considered "opposite" to a Poisson distribution? or how about a negative Poisson distribution where the lambda variable is negative?

As you can probably tell, I am no mathematics genius but I enjoy trying to work things like this out.

Does anyone have any insights they would like to share? I welcome the simplest to the most complex ideas (even if I may not understand them straight away).

Looking forward to hearing any ideas.

Oh, I hope I posted this in the right spot. I read the forum rules about posting to the most appropriate category so this is what I decided upon. Sorry if it should be elsewhere.

2. Originally Posted by JavaJunkie
Hello,
This is my inaugural post on this forum. Without giving my life story, I would like to say that I am in no way mathematically savvy and the highest level that I have "properly" studied mathematics is year 12 maths B. In saying that though I have a rather keen interest in mathematics and like to study it in my spare time.

I was wondering if someone who is actually good at maths could share their insight on the following (ill-defined)problem.

A company has employed the following number of people over the last 12 months (June hires, July hires, ........, April, May):

30, 40, 60, 20, 34, 61, 58, 42, 39, 56, 59, and 48. So obviously the total for the year is 547 and the average number of hires per month is roughly 45.48.

At the same time the number of firings over the last year is (June hires, July hires, ........, April, May):

43 ,62 , 23, 59, 50, 34, 48, 25, 43, 36, 25, 56. Again the total is 504 and the average firings per month is 42.

I was wondering if there was anyway that these figures could be used to predict the probability of how many hires and/or terminations would be made in 1 month's time, 2 months time, 12 months time, n months time?

When considering this I've come up with a few ideas based upon the things I know about probability distributions (which, albeit, is very little).

First of all I was thinking that for the number of people employed, a Poisson distribution could be used, where the lambda variable is the mean of all employment numbers at a monthly level because it is my understanding that a Poisson distribution tracks "movement in".

But then it crossed my mind that what if the number of hires were conditional on the number of terminations? Could some conditional probability be used?

But that begs the question, how could one determine if the hires and firings were either dependent or independent?

Also, if the hires did have a Poisson distribution, what sort of distribution could the terminations have? Is there something that could be considered "opposite" to a Poisson distribution? or how about a negative Poisson distribution where the lambda variable is negative?

As you can probably tell, I am no mathematics genius but I enjoy trying to work things like this out.

Does anyone have any insights they would like to share? I welcome the simplest to the most complex ideas (even if I may not understand them straight away).

Looking forward to hearing any ideas.

Oh, I hope I posted this in the right spot. I read the forum rules about posting to the most appropriate category so this is what I decided upon. Sorry if it should be elsewhere.
You might want to look at the cross-correlation of the two time series.

CB