How can SAS generate a dataset containing random realization of a negative binomial distribution with noise?

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To generate a dataset containing random realization of a negative binomial distribution with noise in SAS, you can use the following steps:

1. Specify the parameters for the negative binomial distribution, such as the mean and variance or mean and dispersion parameter.

2. Use the SAS PROC SURVEYSELECT procedure to generate a dataset of random noise. The procedure can be used to generate random samples of a specified size and distribution.

3. Add the generated noise to the random realization of the negative binomial distribution to create the final dataset. You can use the SAS DATA step to perform this operation.

Here is an example code:

/* Specify the parameters for the negative binomial distribution */
data parm;
  mu = 10; /* mean */
  phi = 1.5; /* dispersion parameter */
run;

/* Generate a dataset of random noise */
proc surveyselect data=parm out=noise
                method=urs n=100 seed=12345;
  var mu;
  weight phi;
  select mu;
run;

/* Generate a dataset of negative binomial distribution */
data nb;
  do i=1 to 100;
    x = rand("negbin", mu, phi);
    output;
  end;
run;

/* Combine the datasets of negative binomial distribution and noise */
data final;
  merge nb noise;
  y = x + mu; /* add noise */
  drop i mu phi;
run;

In this example, we first specify the mean and dispersion parameter for the negative binomial distribution in the PARM dataset. We then use PROC SURVEYSELECT to generate a dataset of random noise, based on the mean and dispersion parameter in the PARM dataset. The SURVEYSELECT procedure generates 100 random samples of the given distribution (in this case, a normal distribution) and combines them into a single dataset called NOISE.

Next, we generate a dataset of negative binomial distribution with 100 observations, using the mean and dispersion parameter in the PARM dataset. The RAND function is used to generate a random realization of the negative binomial distribution.

Finally, we use the SAS DATA step to merge the datasets of negative binomial distribution and noise, and add the noise to the negative binomial distribution to create the final dataset called FINAL. The final dataset has two variables: X, which represents the random realization of the negative binomial distribution, and Y, which represents X plus the noise generated in the NOISE dataset.