# Reg: Best fit

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This topic contains 11 replies, has 5 voices, and was last updated by Salomon 14 years, 11 months ago.

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- October 18, 2004 at 3:50 pm #37252
I Have a Hourly arrival data, that is two parameters one is 24 hours in a day and the other is No. units Arriving every Hour, I want to try a best fit proability distribution for this so that I can arrive at an expression which would be taken as a regular arrival pattern every hour. Am i correct or can there be anything else done or suggest me what all I can do to get what I nee.

0October 19, 2004 at 5:22 pm #109366

John J. McDonoughParticipant@John-J.-McDonough**Include @John-J.-McDonough in your post and this person will**

be notified via email.Ramesh

This is a little trickier than just “fit a line”.

You know going in that your data will be cyclical. Very likely, it will be cyclical over a 168 hour cycle, but most likely, over 120 of those 168 hours, there will be a 24 hour cycle, but not necessarily exactly the same for each weekday. Most likely the weekends will be different, or maybe you don’t count weekends which can simplify your task a little.

You need to look at your data, lots of data. Run your fingers through it until you are intimate with it. Then perhaps you can propose the form of a function that you can fit to the data.

Once you have some credible function, now you can fit the function to your data. Will the result be meaningful? Probably not. Will it be useful? Possibly.

–McD

0October 19, 2004 at 6:09 pm #109371Hello Mr. Mc. D

I understand your point well but what exactly iam trying to do is I have all the days same no. shifts and same no. of people so what i feel is theres no much variation and i totally agree with you but right now for my analysis and the same will be applied further be Used for Simulation based onthis arrival pattern.

So considering 7 days as Common I want to analayze the arrival pattern and arrive at a certain probabilty distribution.

which i can either do with Excel or SPSS with these I am familiar with so please let me know what I can do I have tried certain methods but I am not happy with the results i amgetting.

Bye!0October 19, 2004 at 6:30 pm #109373

John J. McDonoughParticipant@John-J.-McDonough**Include @John-J.-McDonough in your post and this person will**

be notified via email.Ramesh

What function are you trying to fit? It doesn’t really matter what particular program you have doing the math, the real question comes down to what math are you asking it to do?

If you are simply asking Excel, for example, to run a regression of arrivals against hour, of course the result won’t be very satisfying. You know up front that’s not what you have.

Go off and grab the following report:

http://www.qsl.net/wb8rcr/NTS/Seasonality%20Regression.pdf

This is basically solving the same problem you are dealing with, in a sort of brute-force way. Here the data is annual rather than daily, but the basic problem is the same.

As I said earlier, doing this sort of thing may not be all that meaningful in a purist sense, but the results might turn out to be helpful, nonetheless.

What you need to do is to figure out what form the result should take. I can’t imagine that it would be a straight line, or even a polynomial, against hour of the day. More likely it is some sort of cyclical function, so step one is understanding what the data looks like well enough that you can propose some appropriate function.

Presuming you don’t want to spend your life doing higher math, but simply want a useful model, step two is to transform your data so you can do a regression against something (like a straight line) that you can do with the tools at your disposal. This is where Excel is really handy.

Without actually seeing your data I am leaping to some conclusions here, so it is very important that you really get to know your data so you can draw enlightened conclusions.

If you would like to discuss this a little more directly, please feel free to email me at mcd@is-sixsigma.com.

–McD

0October 19, 2004 at 6:33 pm #109374

John J. McDonoughParticipant@John-J.-McDonough**Include @John-J.-McDonough in your post and this person will**

be notified via email.I see the posting software munged up the URL I sent, you will need to copy and paste it into your browser rather than trying to click on it.

–McD

0October 19, 2004 at 9:08 pm #109383Hello Mr McD,

I am Loking at the URL you sent.

As I said I am a little bit confused let me explain you clearly what I amtrying to do:

I have data which is in two Columns one is Hours and the second is Total No. of arrivals( could be anything) I have plotted a chart for Hours Vs Total No. of Arrival every Hour and once I got the bar chart I want to draw a best fit line which gives me an expression, a Probabiltity Distribution which I can further use as my arrival pattern and the Data Considered for this is for 15days I mean two weeks.

And I am not able to which can be a best fit form Math point of view?and I can say I dont know How exactly I can Best Fit my available Data.

Thanks,BYe,Ramesh!0October 20, 2004 at 12:18 am #109389Ramesh,You might consider “Fourier Analysis”. It is a standard mathematical technique to fit a curve to periodic data. If you could post the data, or email it to me, I could take a quick look at it.Tim F

0October 20, 2004 at 1:12 am #109390Hi ,

If I get your e-mail Id I can defintiely send you the data and it would be of very good help but I would like to try it myself before once.

Thanks

Ramesh!0October 20, 2004 at 4:09 am #109391RameshMy email is tjfolkerts@yahoo.com

Tim F0October 20, 2004 at 5:02 pm #109412Hello Mr Tim and Mr. John ,

I have sent you the data file and I guess that should give you a better idea of what i am trying to do.Please let me know what all I could do with that Data.

Thanks

Ramesh!0October 25, 2004 at 12:43 pm #109635If you have Minitab, try Stat > Quality Tools > Individual Distribution Identification. In the output, look for distributions with a p-value greater than .05 (assuming a 95% confidence level) and choose the one with the smallest Anderson-Darling (A-D) Statistic. If none of them fit, you may want to break your data down into smaller “chunks”, because you may have several different arrival rates happening at different times of the day.

Good luck!

0November 1, 2004 at 2:16 pm #110073Hi there,

There is a special case for what you are tryin to do. Arrivals are best studied by its reciprocal, the time between arrivals, which ties up with another interesting effect (which you have discussed earlier, with other words – the effect of the day, hour – peak interval): stationary rates of arrival. To fully understand your process, you must have the exact time of the individual arrival, if arrivals cannot be separated (ie, arrived in batches or exactly at the same time, no difference whatsoever) then we can categorize the arrival time and the batch size.

Once with that, calculate the interarrival time and plot it, create a histogram (frequency) as well. You must find the time intervals for which your process is stationary – the interval in which the average rate of arrival has not shifted. Normally, you would be interested in studying peak hours or peak days, since it will yield the worst case capacity estimations. Regardless of the distribution, the average rate of arrivals is the inverse of the average interarrival time, for a stationary period.

Now, you can use whatever technique or sw app to try and fit a distribution (not a regression, please… the process is stochastic, right? so don’t use a deterministic model). Interarrivals times in most human activities are independent and exponentialy distributed, thus making the arrivals distributed Poisson, with the average 1/b, being b the average interarrival time.

Hope this helps

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