ECDF Plot: See the Full Cumulative Distribution of Your Data
What is an ECDF Plot?
The empirical cumulative distribution function sorts the data and sets the height at any value x to the proportion of observations less than or equal to x; it is an unbiased estimate of the population distribution F(x) and requires no distributional assumptions. As the sample grows, the ECDF approaches the true distribution, so it supports quantile reading and distribution comparison and is the standard non-parametric tool for visualizing distributions. It is the bridge between empirical data and theoretical distributions.
When to Use It
Use an ECDF for a distribution overview without distribution assumptions, for reading any percentile such as P95 or P99, for comparing two data sets with the KS test, and as the visual basis for goodness-of-fit evaluation. Because the ECDF has no binning parameter and loses no information, it is more objective than a histogram for exact comparison. Reading extreme quantiles such as P95 and P99 is especially stable with an ECDF.
How to Use It (Step by Step)
Paste one or more data columns; the tool draws the step-plot ECDF for each group and can overlay a theoretical distribution curve. Read the plot: steeper segments mean denser data, the height at any x is the cumulative proportion, and separation between two ECDF curves indicates different distributions. Overlay multiple ECDFs to see exactly where and how much distributions differ, and confirm formal comparisons with the KS test.
Key Formulas / Example
The ECDF at x is Fn(x) = (number of observations less than or equal to x) / n, a step function that jumps by 1/n at each data value. The 95th percentile is the x where Fn(x) first reaches 0.95, and the tool lets you enter a proportion directly to read the corresponding quantile. To judge normality, overlay the theoretical normal CDF: clear deviation from the curve means non-normality, which a normality test then confirms.