Zipf Rank-Size Exponent Checker
Test a city against the Zipf rank-size rule and report how far its population deviates in percent.
Description
Test a city against the Zipf rank-size rule and report how far its population deviates in percent.
Zipf Rank-Size Exponent Checker is a focused tool for the following task. Test a city against the Zipf rank-size rule and report how far its population deviates in percent. It reports Deviation, Within tolerance from the values you provide rather than inventing measurements, coefficients, or professional judgment that are not part of the input.
When to use Zipf Rank-Size Exponent Checker
Use this sociology calculation to reproduce a named demographic, inequality, mobility, urban, or survey measure when the population, period, categories, and coding rules are explicit.
- City population
- Required number. Observed population of the ranked city.
- Rank
- Required integer. Rank of the city within the urban system.
- Largest city
- Required number. Population of the largest city in the system.
- Zipf exponent
- Optional number. Zipf exponent; one is the classical rank-size rule.
The cited overview of Sociology supplies background for the terminology and domain context used by this tool.1
How Zipf Rank-Size Exponent Checker works
Test a city against the Zipf rank-size rule and report how far its population deviates in percent. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.
- Deviation (%)
- Returned number in %. Observed minus expected size relative to expected.
- Within tolerance
- Returned boolean. Whether the absolute deviation stays inside ten percent.
Limitations and assumptions
- Definitions, sampling error, missing data, historical context, geographic boundaries, weighting, and classification choices can materially change social indicators and their interpretation.
- City population must be at least 0.
- Rank must be at least 1.
- Rank must be no greater than 1000000.
- Largest city must be at least 5e-324.
- Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.
Alternative or Complementary approaches
Report the source population and uncertainty, inspect disaggregated data, and compare multiple accepted indicators rather than treating one summary statistic as a complete social explanation.
References
-
Sociology — Wikipedia contributors
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