Estimating values from kurtosis and skewness

If I know the size of a population, the number of categories/labels, and the skewness and kurtosis of the distribution, is it possible to estimate the number of items which fall into each category?

For example, given the data set:

category A: 11
category B: 13
category C: 15
category D: 22
category E: 33
category F: 15
category G: 5

I know that there are 114 items in the population, a skewness of 1.05 and a kurtosis of 1.56.

Is there any way to reverse this and get an approximation of the values? If I know the population size of 114 and the skewness and kurtosis values, can I somehow approximate the values in each category?