topic Re: question in SAS Programming

question about the mixture of two normal distributions

librasantosh — Fri, 15 Dec 2017 11:04:04 GMT

Data generated using random number with Normal distribution (mean=5 std=2) as dataset D1 which has 100 elements.

Data generated using random number with Normal distribution (mean=3 std=3) as dataset D2 which has 80 elements.

Based on D1 and D2, data generated with Normal distribution at 30% Normal (mean=5, std=2)+70% Normal (mean=3, std=3) as D3 which has 120 elements

How to estimate proportion of D1 and D2 in dataset D3?

question on estimating proportions

librasantosh — Thu, 14 Dec 2017 15:24:01 GMT

Data generated using random number with Normal distribution (mean=5 std=2) as dataset D1 which has 100 elements.
Data generated using random number with Normal distribution (mean=3 std=3) as dataset D2 which has 80 elements.
Based on D1 and D2, data generated with Normal distribution at 30% Normal (mean=5, std=2)+70% Normal (mean=3, std=3) as D3 which has 120 elements

How to estimate proprotion of D1 and D2 in dataset D3?

If any idea please let me know.

Re: question

Reeza — Thu, 14 Dec 2017 02:28:52 GMT

Two ways pop to mind:

1.Simulation

2. Theory — look at joint distribution probability and see.

The correct method is likely what you’ve been taught in the course. If it’s theoretical, check your text, this isn’t a SAS question.

If it is simulation, what do you have so far?

I also feel like the question may be missing something...Is this the word for word question from your assignment or have you paraphrased it?

@librasantosh wrote:

Data generated using random number with Normal distribution (mean=5 std=2) as dataset D1 which has 100 elements.

Data generated using random number with Normal distribution (mean=3 std=3) as dataset D2 which has 80 elements.

Based on D1 and D2, data generated with Normal distribution at 30% Normal (mean=5, std=2)+70% Normal (mean=3, std=3) as D3 which has 120 elements

How to estimate proportion of D1 and D2 in dataset D3?

PS asking the same question multiple times is unhelpful.

Re: question

PGStats — Thu, 14 Dec 2017 04:13:33 GMT

Proc FMM (Finite Mixture Models) does this kind of estimation.

Re: question

librasantosh — Thu, 14 Dec 2017 13:14:47 GMT

thanks for reply

Re: question

Rick_SAS — Thu, 14 Dec 2017 15:50:52 GMT

Not clear if you want to do this in SAS or if it is a theoretical question....

If in SAS, it sounds like you are simulating a random sample from a mixture of normal distributions. However, your question seems to imply that the data set that you want is a random mixture of SAMPLES, where the samples are obtained beforehand.

Anyway, if you read the article, you will see that the general technique is

1. Generate random Bernoulli variate:

b = rand("Bern", 0.3);

2. Use the 0/1 value to determine if you should choose a random sample from the first or second distribution.

I think what I would do is use PROC SURVEYSELECT (or, easier, PROC IML) to sample 120 elements from each data set with replacement. Then merge the results and use the above technique to get your simulated sample:

If this is a theoretical question, the answer is to look at the expected value of the proportions. You expect 0.3*120 = 36 observations from D1 and 0.7*120 = 84 observations from D2.Use those values and the sizes of D1 and D2 to answer the question.

Re: question

Gunther — Fri, 15 Dec 2017 10:34:41 GMT

Congratulations Rick_Sas for all your badges !

Add me as a friend ?

Re: question

Rick_SAS — Fri, 15 Dec 2017 11:03:08 GMT

You can add me as a friend. That enables you to get notified (if you wish) on my activity, such as when I answer a question.

Re: question

Gunther — Fri, 15 Dec 2017 11:04:46 GMT

Thank you Rick, you're really the best !

Re: question on estimating proportions

StatDave — Tue, 19 Dec 2017 15:52:16 GMT

Sounds like a job for PROC FMM. Given data set D3 with response values in Y:

proc fmm;
model y = / k=2;
run;