Intersection of two normal distributions 2

[Robbyod]

Hi all,
I am trying to find formulae for calculating the overlap between two normally distributed populations.
There are some online calculators specifically for this but they do not have the resolutinion i require.

So for M1,?1 and M2,?2, (where M is Mean and ? is StDev) what formula will give me the probability of samples from these populations overlapping.

Im trying to find the % interferance fit between an OD and ID

I have been using JMP so far as a stop gap but i know this is not entirely accurate, the method below is what im using

by finding the % of Group 2 below the point M1+3(?1) and vise versa, then multiplying the two %

M+3(?) still leaves 0.15% of the population unacounted for and i want a more accurate result.

Your comments on a better fast method aswell as the formuala are welcome and appraciated

Thanks

 

[IRstuff]

Seems to me that you should red-flag this posting and repost in a more obvious forum forum1103. Have you even done a search?

TTFN

FAQ731-376

 

[magoo2]

I think it's a legit question for this forum. I wasn't aware of the one on Drafting Standards and that doesn't sound like a good fit to me.

I'd be tempted to start with something like a 2 sample t-test with the data.

 

[IRstuff]

The OP's question pertains to "% interferance fit between an OD and ID" which seems to be a tolerancing problem.

TTFN

FAQ731-376

 

[Robbyod]

While the underlying issue is a tolerance issue, the question and its specifics are statistical, which is why i chose this forum.

So, does anyone have any ideas?

 

[GregLocock]

http://mathworld.wolfram.com/Convolution.html

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[Robbyod]

Thanks guys, what i did in the end was create an excel template which will calculate the % overlap of two data sets which can be pasted in.

Much easier than running through differential equations.

The template is giving me almost identical answers to the estimations i made with JMP (identical down to 2 decimals)

It will calculate the overlap between the two points 3 sigma from the mean in each population so there is still a minute % unnacounted for.

The template is attached below if anyone would like to use it.

 

[Robbyod]

Sorry, the file attachment function doesnt seem to be working

 

[PaulJackson]

((M1-M2)/sqrt(?1^2+?2^2))
Paul