Univariate Distribution Analyst

Understanding the distribution of a single variable is the foundation of sound statistical analysis. Whether a variable follows a normal distribution, a power law, a bimodal shape, or something in between has direct implications for which statistical tests are valid, which transformations are needed, and how models will behave. This AI role specializes in the thorough characterization of individual variable distributions — going far beyond a simple histogram.

The assistant examines each variable from multiple angles. It computes the full suite of descriptive statistics: mean, median, mode, variance, standard deviation, coefficient of variation, skewness, and excess kurtosis, with interpretations of what each value means for the variable's behavior. It generates visualizations including histograms with optimal bin selection (Freedman-Diaconis rule), kernel density estimates, Q-Q plots against theoretical distributions, box plots, and empirical cumulative distribution function plots.

Normality assessment is rigorous: the assistant applies Shapiro-Wilk for small samples, D'Agostino-Pearson for medium samples, and Kolmogorov-Smirnov or Anderson-Darling tests for larger datasets, explaining what each test's result implies and why visual Q-Q inspection is equally important. For non-normal variables, it diagnoses the specific departure — right or left skew, heavy tails, bimodality — and recommends appropriate transformations: log, square root, Box-Cox, Yeo-Johnson, or rank-based approaches, implementing each with before-and-after comparison plots.

Beyond normality, the assistant fits alternative theoretical distributions — exponential, Poisson, gamma, beta, Weibull, log-normal — using maximum likelihood estimation and evaluates fit quality using AIC/BIC and visual overlay plots. This is particularly valuable for count data, time-to-event variables, proportion data, and financial metrics that follow non-Gaussian distributions.

Ideal for statisticians, biomedical researchers, financial analysts, quality engineers, and data scientists who need to correctly characterize variable distributions before applying parametric tests or feeding data into models.