'high-kurtosis' is a compound of 'high' and 'kurtosis'. 'high' originates from Old English 'heah' meaning 'tall' or 'elevated'. 'kurtosis' was coined in modern statistics from New Latin/Greek elements, ultimately from Greek 'kurtos' meaning 'arched' or 'curved'.

'kurtosis' was introduced into statistical English in the late 19th / early 20th century (notably by Karl Pearson and other statisticians) from Greek-rooted coinage; 'high' developed from Old English 'heah' through Middle English into the modern word 'high'.

Initially related to the idea of 'curvedness' or 'peakedness' (from the Greek root), 'kurtosis' in statistics came to denote a numeric measure of a distribution's peak and tail weight; 'high-kurtosis' thus evolved to emphasize heavy tails and/or a sharp central peak relative to the normal distribution.