Overview
Distribution fitting is not a matter of trying every distribution and picking the one with the best fit statistic. The right distribution is constrained by the data-generating process: count data cannot follow a normal distribution, bounded proportions cannot follow an unbounded distribution, heavy-tailed financial data cannot be adequately modeled by a normal distribution that underestimates tail probabilities.
The consequence of fitting the wrong distribution is not just a poor statistical fit — it is wrong risk estimates. A normal distribution fitted to financial returns underestimates the probability of extreme losses by orders of magnitude. A Poisson distribution fitted to overdispersed count data underestimates variance and produces confidence intervals that are too narrow.
The Distribution Fitting & Goodness-of-Fit Prompt generates a complete distribution fitting framework: candidate selection by data type and shape, parameter estimation, goodness-of-fit testing with multiple criteria, and a business application that uses the fitted distribution for probability calculations, risk quantification, and Monte Carlo simulation.
What you get: - Candidate distribution selection by data type and shape - Maximum likelihood parameter estimation - Goodness-of-fit testing with multiple criteria - Distribution comparison and selection - Business application (probability calculations and simulation)
Built for: analysts, risk managers, and data scientists who need to fit probability distributions to data for risk quantification, simulation, and probabilistic modeling.