Due to the lack of analytical expressions for the quantiles of finite mixture models, a reliable computational method is required for practical applications of mixture models. This paper focuses on numerical computations of quantiles of finite mixtures in which mixture components are stochastically ordered. As an alternative to single-step root-finding approaches, we propose a recursive algorithm in which, at each step, the quantile of the given mixture is expressed as the quantile of another mixture with one less component than the original mixture at a revised quantile level. To deal with numerical instability when the quantile level is close to either one or zero, we consider the forward, backward and combined methods for sequential updating. The proposed methods are illustrated with three size-biased mixture distributions: Erlang mixture, size-biased Weibull mixture and size-biased truncated lognromal mixture.
T. Bae (Sat,) studied this question.