Comparing observed and theoretical distributions

In this talk, I aim to discuss tools to compare the observed distribution of a variable with the theoretical distribution assumed by a model. In particular, I will focus on the situation where a model assumes a certain distribution for the explained/dependent/y variable and one or more parameters of this distribution, often the mean, change when one or more explanatory/independent/x variables change. The challenge is that the dependent variable no longer follows the theoretical distribution, but rather follows a mixture of these theoretical distributions. In the case of a linear regression, we can circumvent this difficulty by looking at the residuals, which should follow a normal distribution. However, this circumvention does not generalize to other models. I will show the margdistfit package, which graphically compares the distribution of the dependent variable with the theoretical mixture distribution.