Analyze

Distribution Fit

Fit data to multiple distributions and rank by Goodness-of-Fit test

Methodology

Distribution fitting tests which statistical distribution best matches a given dataset. This module tests 7 distributions: Normal, Log-Normal, Weibull, Exponential, and Gamma (continuous) plus Poisson and Binomial (discrete).

Workflow

Detect data type: auto-detection (all integers → discrete, otherwise continuous) or manual selection
Parameter estimation: Maximum Likelihood / Method of Moments for each distribution
Goodness-of-Fit: Kolmogorov-Smirnov (continuous) or Chi-Squared (discrete)
Ranking by p-value: highest p-value = best fit
Normality deep-dive: Shapiro-Wilk, Anderson-Darling, Jarque-Bera, D'Agostino-Pearson

Tested Distributions

Distribution	Type	Parameters	Typical Use
Normal	Continuous	μ, σ	Measurements, tolerances, natural variation
Log-Normal	Continuous	μ_log, σ_log	Cycle times, income, particle sizes
Weibull	Continuous	k, λ	Lifetime, failure analysis
Exponential	Continuous	λ	Wait times, failure rates
Gamma	Continuous	α, β	Wait times, aggregated Poisson processes
Poisson	Discrete	λ	Defect counts, events per time unit
Binomial	Discrete	n, p	Pass/Fail, scrap rate

Example

A manufacturing process produces cycle times in seconds. The data shows right skewness — typical for log-normal distributions.

Load dataset (example: cycle times)
Run analysis → ranking shows Log-Normal as best fit
K-S test p-value > 0.10 → distribution fits well
Normality deep-dive shows Normal is rejected

Result: For control charts and capability analysis, data should be log-transformed before applying standard methods.

Interpretation

p-Value Assessment

p-Value	Assessment	Recommendation
≥ 0.10	Good	Distribution fits — do not reject
0.05 – 0.10	Borderline	Use with caution, larger sample recommended
< 0.05	Poor	Distribution does not fit — reject

Normality Consensus

The module runs four specialized normality tests and forms a consensus verdict. Shapiro-Wilk is the gold standard for small samples, Anderson-Darling is especially sensitive in the distribution tails, Jarque-Bera is an asymptotic test based on skewness and kurtosis (ideal for n > 30), and D'Agostino-Pearson reveals why normality fails (skewness vs. kurtosis).

Common Pitfalls

Small sample size: GOF tests have low power when n < 30. A non-significant result does not mean the distribution fits.
Multiple testing: 7 distributions are tested simultaneously — the best fit may look good by chance. Always check substantive plausibility.
Ignoring data type: Poisson/Binomial only meaningful for integer count data. Do not test continuous data as discrete.
p > 0.05 ≠ proof: A high p-value does not prove the distribution is correct — it only says the data do not contradict it.
Outliers: Individual extreme values can heavily bias parameter estimates. Check for outliers before fitting.

Examples

This module ships with the following example datasets — load any of them in the app with a single click.

Fit normal distribution — Project template

80 values from N(μ=10, σ=2) — clean textbook normal distribution. Shapiro-Wilk / Anderson-Darling should not reject H₀.

Fit Weibull lifetimes — Project template

80 component lifetimes from Weibull(k=2.5, λ=100 h). Classic wear-out case (β > 1); Weibull should rank as best fit.

Fit lognormal cycle times — Project template

80 cycle times from Lognormal(μ_log=ln 5, σ_log=0.6) — strongly right-skewed. Distribution-fit should rank lognormal first.

Fit exponential waiting times — Project template

80 waiting times from Exponential(μ=15 min) — memoryless distribution. Exponential and gamma rank highest.

Available in the following cycles

DMAIC: Analyze
DMADV: Analyze
8D: D4 — Root Cause Analysis