About Distribution Analyzer

Analyze probability distributions and statistics. Part of the DevTools Surf developer suite. Browse more tools in the Statistics collection.

Use Cases

• Determine which probability distribution best fits latency or response time data
• Test whether survey response data is normally distributed before applying parametric tests
• Analyze business metrics (revenue, customer size) for log-normal patterns
• Identify heavy-tailed distributions in financial returns or error rates

Tips

• Enter a dataset as comma-separated values or paste a single column of numbers — the analyzer fits multiple distributions (normal, log-normal, exponential, Poisson) and reports goodness-of-fit
• Use the Q-Q plot to visually assess normality — points deviating from the diagonal line indicate non-normal distribution tails
• Check skewness and kurtosis values alongside the distribution fit — skewness > 1 or kurtosis > 3 significantly affects which statistical tests are appropriate

Fun Facts

• The normal (Gaussian) distribution was independently discovered by Abraham de Moivre in 1733 and later redescribed by Gauss in 1809. Gauss used it to describe measurement errors in astronomical data — the first practical application of what became the most important distribution in statistics.
• The central limit theorem (CLT) explains why the normal distribution is so ubiquitous: the sum (or mean) of a large number of independent random variables converges to a normal distribution regardless of the original distribution. This applies to sample means from virtually any distribution with finite variance.
• The Pareto distribution, often called the '80/20 rule' after Pareto's 1906 observation that 80% of Italy's land was owned by 20% of the population, is a power law distribution. Wealth, city sizes, earthquake magnitudes, and web traffic all follow power law distributions rather than normal distributions.

FAQ

Why does it matter which distribution my data follows?

Most parametric statistical tests (t-test, ANOVA, Pearson correlation) assume normally distributed data. If your data is log-normal, exponential, or has heavy tails, these tests produce inaccurate results. Distribution-appropriate tests or transformations are required.

What is skewness and kurtosis?

Skewness measures asymmetry: 0 = symmetric, positive = right-skewed (long right tail), negative = left-skewed. Kurtosis measures tail heaviness: normal distribution has kurtosis 3 (or excess kurtosis 0). Higher kurtosis means more extreme outliers than normal.

How do I test if my data is normally distributed?

Visual: histogram, Q-Q plot, box plot. Statistical tests: Shapiro-Wilk (best for small samples, n<50), Kolmogorov-Smirnov (large samples), Anderson-Darling. All tests have power limitations — large samples will reject normality for trivially small deviations. Use judgment alongside tests.