Reference

After a fit completes the Fitter shows four pieces of evidence: the histogram + PDF overlay, the diagnostics row (Q-Q, P-P, CDF), and the ranked candidates table. This page lists what each column and chart reading means.

tip

Use the AI tab on the right to talk through any of this in plain language. Try "Why is lognormal ranked above gamma here?" or "What does this Q-Q plot tell me?"

The ranked candidates table

This is the headline output. Each row is one candidate distribution with its fitted parameters and a battery of goodness-of-fit numbers.

Column	Meaning
Distribution	The candidate's canonical name.
Parameters	Fitted parameters in the canonical form used across PocketStats.
AIC	Akaike Information Criterion. Lower is better. Primary sort key. Penalizes parameter count, so simple distributions aren't unfairly punished.
BIC	Bayesian Information Criterion. Lower is better. Heavier penalty for parameter count than AIC; useful for tie-breaking.
KS stat	Kolmogorov–Smirnov statistic. Lower is better — measures the largest gap between fitted and empirical CDFs.
AD stat	Anderson–Darling statistic (continuous fits only). Like KS but more sensitive to tail mismatches.
p-value	From the KS test. A small p-value (< 0.05) means the fit is statistically rejected; the Fitter flags these with a warning glyph.

Rules of thumb for comparing two candidates by AIC:

• Difference under 2 — essentially the same fit; prefer the simpler distribution.
• Difference of 4 to 7 — positive evidence for the lower-AIC candidate.
• Difference over 10 — strong evidence.

note

For how to read a p-value on a large dataset, and what to do when no candidate fits well, see Core concepts.

The histogram + PDF overlay

The top chart shows the column's empirical distribution as a histogram, with the selected candidate's PDF overlaid as a smooth curve. This is the most direct way to see whether the fit is plausible.

Look for:

• The curve hugging the bulk of the histogram bars
• Matching skew direction (right tail vs. left tail)
• Reasonable behavior at the extremes — neither cut off nor wandering far past the last bar

A fit that nails the center but misses both tails is a sign you've picked a too-symmetric distribution for skewed data. Try lognormal, gamma, or weibull instead of normal.

Q-Q plot (quantile–quantile)

Plots the quantiles of your data against the quantiles predicted by the fit. If the fit is good, points fall close to the diagonal y = x line.

What you see	What it means
Points on the diagonal	The fit matches at every quantile — a strong fit.
Curve bending upward at the right	The data's right tail is heavier than the fit predicts.
Curve bending downward at the right	The data's right tail is lighter than the fit predicts.
S-shape	Skew mismatch — try a more or less skewed distribution.

The Q-Q plot is the single most useful diagnostic for continuous fits. Tail deviation is the most common failure mode and it shows up clearly here.

P-P plot (probability–probability)

Plots the empirical CDF against the fitted CDF at each observed point. Like Q-Q, a good fit hugs the diagonal — but P-P is more sensitive to the body of the distribution than to the tails.

If Q-Q looks good but P-P doesn't, the fit captures the extremes but is off in the bulk. The other way around (P-P good, Q-Q bad) means the body is right but the tails are wrong — which is typically the more important problem for simulation.

CDF overlay

Plots the empirical CDF (a step function from the data) and the fitted CDF (a smooth curve) on the same axes. Easy to read at a glance: where the two curves separate, the fit is wrong.

This is the visual analogue of the KS statistic — the KS number is just the largest vertical gap between these two curves.

Supported distributions

The Fitter's candidate set is the same vocabulary used by Process Map, Spreadsheet Sim, and Probability Playground — so anything you fit can be inserted into any of those tools without re-parameterizing.

Continuous distributions

Distribution	Parameters	Typical use
normal	mean, std	Symmetric values scattered around a center — measurement noise, test scores, height.
lognormal	mean, std	Right-skewed positive values — revenue, task durations, file sizes.
exponential	scale	Time between independent events — inter-arrival times, time-to-failure. scale is the mean.
uniform	low, high	Equally likely anywhere in a range — randomized timing, anonymized IDs.
triangular	left, mode, right	Three-point estimate when you have low / most-likely / high judgments rather than data.
gamma	shape, scale	Flexible right-skewed positive distribution — waiting times, rainfall.
weibull	shape, scale	Reliability and wear-out modeling — component lifetimes.
beta	alpha, beta	Bounded in [0, 1] — proportions, conversion rates, percentages.
erlang	k, scale	Sum of k exponentials, with integer k — service times in queueing models.

Discrete distributions

Distribution	Parameters	Typical use
poisson	mu	Counts of independent events in a fixed window — daily orders, support tickets. mu is the mean count.
binomial	n, p	Successes in n independent trials with probability p — defects per batch.
negative_binomial	n, p	Overdispersed counts (variance > mean) — call volume by day, sales per rep.
geometric	p	Number of trials until the first success.
rounded_uniform	low, high	Integer-valued uniform between low and high inclusive.

A note on lognormal parameters

PocketStats uses output-space mean and std for the lognormal — these are the mean and standard deviation of the values themselves, in their natural units, not the mean and std of log(values).

Each consumer tool (Process Map's sim engine, Spreadsheet Sim, Probability Playground) converts output-space to log-space at its own sampling boundary. You never have to do the conversion yourself.

See Core concepts for why the Fitter uses output-space parameters instead of the log-space convention (μ, σ) used by most lognormal reference material.

A note on exponential parameters

The Fitter and the consumer tools all use scale (the mean inter-event time) as the canonical exponential parameter. Some legacy configs use rate instead; the system accepts either and converts as needed (scale = 1 / rate).

Excluded by design

The Probability Playground also supports a few distributions the Fitter intentionally doesn't try, because they can't be inferred from raw data:

• choice — picks from a fixed list of values
• integers — uniform integer range without bounds inferred from data

If you need either of these in a simulation, define them directly in Playground or as a Process Map distribution rule; the Fitter is for fitting distributions to data.

Next steps

• How-to — once you've picked a fit, save it and use it across tools