A note on the variance of a lightly trimmed mean when multiple outliers are present in the sample

In this note, a recurrence relation for product moments of order statistics arising from independent and non-identically distributed variables is utilized to derive a convenient formula for the variance of a lightly trimmed mean when one or more outliers are present in the sample. Formulas are presented for the two cases when: (i) the outliers are scale-outliers, and (ii) the outliers are location-outliers. Two examples are given to illustrate the usefulness of the formulas derived in this note.