ECDF Plot Calculator for Machine Learning

ECDF result

Load data, then select Calculate ECDF.

Click a plotted point to inspect its value and cumulative probability.

Datasets

Choose file

Value column

Weight column

Dataset name

No file loaded.

Data preprocessing

Transformation

Minimum allowed value

Maximum allowed value

Round decimal places

Winsorize each tail (%)

Remove duplicate values

Show detail table descending

Plot configuration

Chart mode

Trace display

Step mode

Line width

Marker size

Line style

Chart title

X-axis label

Y-axis label

X-axis scale

X-axis minimum

X-axis maximum

Show percentages

Show gridlines

Reverse x-axis

Show legend

Show observation rug

Show DKW confidence band

Confidence level

Percentiles, thresholds, and annotations

Active dataset

Probability or percentile

Values above 1 are treated as percentages.

Observed value

Preset percentile lines

Custom value line

Custom probability line

Shade range from

Shade range to

Select a query tool to inspect a quantile or cumulative probability.

Theoretical CDF comparison

Distribution

Parameters

Parameter 1

Parameter 2

Custom CDF expression

Use JavaScript Math functions and variable x.

Distribution comparison

Dataset A

Dataset B

Threshold value

Statistical summary

No active dataset

Detailed ECDF table

Rank	Value	Frequency	Weight	Cumulative count	Cumulative weight	ECDF	ECDF percentage
No calculated data.

Export and session tools

Import configuration

Session data stays in this browser unless exported.

Formula used

Fₙ(x) = (1 / n) Σ I(xᵢ ≤ x)

For weighted observations, cumulative weight replaces cumulative count. The result is divided by total valid weight.

Fₙ,w(x) = Σ wᵢ I(xᵢ ≤ x) / Σ wᵢ

The ECDF rises at observed values. Larger jumps indicate repeated values or greater observation weights.

How to use

Paste numeric observations into one or more dataset cards.
Add optional nonnegative weights with one weight per value.
Choose preprocessing, step behavior, scales, and annotations.
Select Calculate ECDF to update every result section.
Use percentile, theoretical, and comparison tools as needed.
Export the graph, tables, report, or reusable configuration.

Example data

Use case	Dataset A	Dataset B	Interpretation
Train-test shift	Training feature values	Testing feature values	A wide vertical gap suggests distribution shift.
Prediction errors	Model A absolute errors	Model B absolute errors	A curve further left generally indicates smaller errors.
Model latency	Baseline milliseconds	Optimized milliseconds	Compare percentiles such as P50, P90, and P99.

Machine learning applications

ECDF plots reveal complete empirical distributions without histogram bins. They help compare features, residuals, predictions, scores, and latency.

Training and testing curves can expose covariate shift. Grouped curves can also support fairness and robustness reviews.

Percentile analysis is valuable for service-level targets. Tail behavior often matters more than averages.

Frequently asked questions

What does an ECDF show?

It shows the proportion of observations less than or equal to each value.

Why use an ECDF instead of a histogram?

An ECDF avoids arbitrary bin widths and displays every observation.

What does a steep ECDF section mean?

Many observations are concentrated within a narrow value range.

How are repeated values handled?

Repeated values create a larger vertical jump at that value.

Can ECDFs compare train and test data?

Yes. Separation between curves can reveal distribution shift.

What is a complementary ECDF?

It shows the proportion greater than each threshold, emphasizing tails.

What is a weighted ECDF?

Each observation contributes according to its assigned nonnegative weight.

What does the KS statistic measure?

It is the largest vertical difference between two cumulative distributions.

Can this calculator estimate percentiles?

Yes. It returns the first value reaching the requested probability.