Jaro–Winkler distance

In computer science and statistics, the Jaro–Winkler distance is a string metric for measuring the edit distance between two sequences. It is a variant proposed in 1999 by William E. Winkler of the Jaro distance metric (1989, Matthew A. Jaro). Informally, the Jaro distance between two words is the minimum number of single-character transpositions required to change one word into the other.

Jaro–Winkler distance uses a prefix scale ${\displaystyle p}$ which gives more favourable ratings to strings that match from the beginning for a set prefix length ${\displaystyle \ell }$.

The lower the Jaro–Winkler distance for two strings is, the more similar the strings are. The score is normalized such that 1 equates to no similarity and 0 is an exact match. The Jaro-Winkler similarity is given by 1 - Jaro-Winkler distance.

Although often referred to as a distance metric, the Jaro–Winkler distance is actually not a metric in the mathematical sense of that term because it does not obey the triangle inequality.

The Jaro distance ${\displaystyle d_{j}}$ of two given strings ${\displaystyle s_{1}}$ and ${\displaystyle s_{2}}$ is

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