# Percentages in utilization of different distributions

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.

• Any example of nonparametric distribution? – user158565 Aug 1 '19 at 13:53
• @user158565 Wiki describes nonparametric statistics as "the branch of statistics that is not based solely on parametrized families of probability distributions (common examples of parameters are the mean and variance). Nonparametric statistics is based on either being distribution-free or having a specified distribution but with the distribution's parameters unspecified. Nonparametric statistics includes both descriptive statistics and statistical inference." Its use in my question was meant to illustrate broader groupings than just families of parametric distributions. – user332577 Aug 1 '19 at 14:11
• distribution $\ne$ statistics. – user158565 Aug 2 '19 at 14:53
• @user158565 Nonparametric distributions are "distribution-free or have a specified distribution but with the distribution's parameters unspecified." – user332577 Aug 9 '19 at 19:30
• So standard normal distribution N(0,1) is not nonparametric distribution because the distribution's parameters are specified. But N(m,1) is nonparametric distribution because it has specified distribution Normal but with the distribution's parameter m (mean) unspecified. Is it correct? – user158565 Aug 9 '19 at 19:44

I'm not entirely aware if something like that exists for all of literature, but rather for specific research communities. I'm in bioinformatics/biomedical informatics research, so examples are niche-specific, but I would guess the same principle applies elsewhere. Review papers are a great place to start since they survey the literature in that field and summarize these methods (and in turn their distributional assumptions) used for research in their respective community.

For example, this paper in Briefings in Bioinformatics:

Developing a ‘personalome’ for precision medicine: emerging methods that compute interpretable effect sizes from single-subject transcriptomes Francesca Vitali, Qike Li, A. Grant Schissler, Joanne Berghout, Colleen Kenost, and Yves A. Lussier Briefings in Bioinformatics

is a lit review in single-subject differential gene expression that gives an overview of many methods (and their corresponding distributional assumptions) used in this field.

This one in IEEE:

Awada, W., Khoshgoftaar, T. M., Dittman, D., Wald, R., & Napolitano, A. (2012, August). A review of the stability of feature selection techniques for bioinformatics data. In 2012 IEEE 13th International Conference on Information Reuse & Integration (IRI) (pp. 356-363). IEEE.

does a comparison of feature selection techniques for bioinformatics data and reviews techniques.

I understand this does not directly answer your question, but hopefully it helps guide you towards papers/resources that will!

• Thanks for your response. The first paper has good breakouts of different methodologies, e.g., table 4, but does not include a percentage distribution of how often these methods are used and reported in published research. That's really what I'm looking for. – user332577 Aug 1 '19 at 17:49