Can I reproduce the data (for research purposes) if I have a small sample of it? I am involved into a research project and over there I have a small dataset with 35 records of data. As the size of dataset is very small, there is a risk that our machine-learning model become overfit and therefore, I need to have more data.
I am wondering, if I can reproduce these data, given that I guess the distribution of data ?
For example, if I guess that the distribution of the data is normal with mean=5 and std=1.3 then I simply generate 10,000 data and then I will use the reproduced data to train my machine-learning model.
I understand that, as the dataset is small, i might have more than one nominate distribution. For example, the data might be matched with Normal, Beta. Then in this case, how can i know which distribution is the best for me ?

Generally speaking, 35 observations is not enough for ML model. You might consider more simple econometric model, for instance, logistic regression for classification problem.
However, there is one solution. I would suggest bootstrap (sampling from 35 observations with replacement) since bootstrap requires no assumptions about the underlying distribution and reproduces distribution from the small sample in larger one. The problem is that sample with 35 observations only might be not representative for underlying distribution of data, so bootstrapped sample might become useless.
