 Solution

Under independent censoring, observation of an event-free individual to $x_i$ contributes the survival probabilityHere $F$ denotes the survivor function as in the paper, rather than a cumulative distribution function. The censoring distribution contributes an additional factor to the full observed-data likelihood, but if it has distinct parameters and the required independence holds, that factor can be omitted when estimating the event-time parameters. A censored observation still conveys that the event time exceeded $x_i$.