Choose interpretable summaries for a Cauchy simulation

Define the task

A Cauchy distribution has a location and a positive scale, but its population mean and variance do not exist. A finite sample still has an arithmetic average and a sample variance. Computing those numbers does not establish finite population moments. Decide in advance which population feature your simulation is intended to recover.

Carry out the check

Use the median for location and the interquartile range for a central spread summary. The theoretical quartiles equal location minus and plus scale, so the IQR is twice the scale. Report simulation summaries for several independent runs if the goal is to illustrate instability. Preserve the random-number seed and generator settings in the analysis record.

Worked hypothetical example

For a hypothetical Cauchy distribution with location 3 and scale 2, the median is 3, the first quartile is 1 and the third quartile is 5. The IQR is 4. A sample mean far from 3 does not by itself indicate a generator error. A truncation rule produces a different distribution and must be included in the simulation specification before interpreting its moments.

Method checked 11 November 2026 against R documentation: The Cauchy Distribution.