Distribution Sketcher
Draw the density shape you have in mind — freehand strokes, exact points, straight segments and bent arcs on a pannable, zoomable plane — and the tool normalises your sketch to area 1 and fits 16 probability distributions to it by Levenberg–Marquardt least squares: normal, lognormal, exponential, gamma, Weibull, Rayleigh, uniform, triangular, scaled beta, Laplace, logistic, Cauchy, Student-t, Gumbel, Pareto and a two-normal mixture. Or paste raw sample values instead: the data is binned into a histogram and every distribution is fitted by maximum likelihood (Nelder–Mead on the log-likelihood), reported with its KS statistic and inspected with a QQ plot. Candidates are ranked by a BIC- or AIC-style score that trades closeness against parameter count, so a five-parameter mixture only beats a plain normal when the data genuinely calls for it. Each result lists its fitted parameters with a thumbnail plot, overlays onto your sketch or histogram in comparison colors, and copies out as text, scipy.stats code or LaTeX.
Runs 100% in your browser — models are trained and computed locally on your device.
Read the full guide to this tool
Notes
- Sketch fits compare the drawn curve, rescaled to unit area, against each candidate’s probability density function pointwise; raw-data fits maximise the log-likelihood ∑ ln f(xᵢ) directly.
- The ranking score penalises each fitted parameter — by ln(n) under BIC, by a flat 2 under AIC — so heavier-tailed or multi-component families must earn their extra parameters with a genuinely better fit.
- The KS statistic is the largest gap between the empirical and fitted cumulative distributions, and the QQ plot compares sample quantiles with fitted quantiles — points hugging the diagonal mean a good fit, tails peeling away mean the family misses the extremes.
- Runs 100% in your browser — models are trained and computed locally on your device.
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