# Creating probability distribution of pre-aggregated Data

I have an aggregated dataframe where each row contains a mean, standard deviation, and sample size N similar to below:

Mean | Stdev | N

$1023 | 1507 | 23$3951 | 4136 | 17

\$864 | 306 | 112

And so on for about 4000 entries. The two histograms below show the distribution of the means, and the distribution of the log-adjusted means, respectively.

I thought about creating N random samples drawn from the Normal(mean, stdev) of each row, but clearly I can't assume they are normal.

I want to fit a probability distribution to the dataframe so I can randomly sample from that estimated distribution. I haven't been able to fit distributions to the regular or log adj distributions because they are bimodal.

How does one typically create the best representative probability distribution of the original dataframe I have?

• You could try to find a distribution which fits the data well enough, for ex. what PauZen suggested. You could try to use rejection sampling to sample from this particular distribution. Jul 8, 2019 at 11:28

Honestly, there is no good way to answer to your problem since the aggregation lost a part of the information forever.