I'm sure that this question has been asked before on CV but, in drilling through many pages of previous CV questions, no matches surfaced. Regardless, I'm confident some observant participant will be able to point me in the right direction.
To clarify, utilization can be associated with choices in basic model assumptions.
Different distributions refers to broad classes or families of probabilistic distributions. For instance, it seems reasonable to guess that the exponential family of distributions are the most widely used assumptions in published research. This family originates with the Bernoulli, the father (mother) of all distributions, and includes the binomial, gamma, beta, chi-square, normal, Weibull, and so on. Then there are the distributions that are not in the exponential family such as Cauchy, alpha-stable, generalized extreme value distributions, etc. One could also classify distributions as parametric, semi-parametric and nonparametric.
These are just a few examples of ways that a response could be categorized. Given a categorization, I'm looking for something like a percentage breakdown in the utilization of such distributional assumptions in published literature and research. Published literature has wide latitude in definition and is not limited to peer-reviewed journal articles, arxiv, PLOS One papers, etc.
What are the workhorses? the most commonly used? the least common? Where am I likely to find such information? Any advice or suggestions which illuminate this question would be most appreciated and helpful.