Skewness, Kurtosis and Entropy Calculator
Calculate population skewness, excess kurtosis and empirical Shannon entropy from a number list. Entropy is reported in bits.
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Skewness, Kurtosis and Entropy Calculator
Calculate population skewness, excess kurtosis and empirical Shannon entropy from a number list. Entropy is reported in bits.
Skewness, Kurtosis and Entropy Calculator
The input is a list of observations. Locale-aware decimal normalization is followed by strict validation of each complete numeric token. At least one finite numeric observation is required. Each item must be a complete decimal or scientific-notation number; mixed text or a nonfinite value rejects the entire input. Limits are 100,000 numbers and 500,000 UTF-16 code units.
The tool reports population moment skewness, population excess kurtosis and empirical Shannon entropy in bits, with finite results rounded to at most 12 significant digits for display. Mean and variance use divisors n, not n-1: standard deviation is sqrt(sum((x-mean)^2)/n), skewness is the mean cubed standardized deviation, and excess kurtosis is the mean fourth standardized deviation minus 3.
Verified example: 1; 2; 3; 4 has mean 2.5 and population standard deviation about 1.1180 internally, producing skewness 0, excess kurtosis -1.36 and entropy 2 bits because all four values occur once. Input 1; 1; 2; 2 produces entropy 1 bit.
When every observation is identical, standard deviation is zero, so skewness and kurtosis are undefined and the tool displays N/A for both; entropy is 0. Numeric values are grouped by exact JavaScript number equality for entropy, without binning or tolerance-based grouping.
Paste the observations, press Calculate and check whether population moments and exact-value entropy match the analysis you intend. The calculator runs in the browser and does not provide sample-corrected skewness, confidence intervals, hypothesis tests, missing-value imputation, weighted data, histograms or financial, medical or legal conclusions.
Only skewness, excess kurtosis and entropy are displayed. Mean and standard deviation are used internally. Enter numeric observations separated by semicolons or new lines, not expressions. Limit: 100,000 numbers and 500,000 UTF-16 code units.
Finite observations do not guarantee a computable result. For nonconstant data, a calculated population variance below 2.2250738585072014e-308, or a non-finite required intermediate result, rejects the entire calculation, including entropy; rescale the data. For identical values or a single observation, skewness and excess kurtosis are N/A and entropy is 0. Display uses at most 12 significant digits; nonzero results with absolute value below 1e-9 or at least 1e15 use scientific notation.
Use spaces, semicolons or new lines between complete numbers, with this page’s decimal mark. If using a recognized thousands format, keep correct three-digit groups, including nonbreaking-space groups. A nonzero literal such as 1e-400 that underflows to zero is rejected; invalid observations are never silently dropped.
Processing takes place locally in your browser.