  \noindent Randomized nomination sampling (RNS) is a rank-based sampling
technique which has been shown to be effective in several nonparametric studies
involving environmental and ecological applications. In this paper, we
investigate parametric inference using RNS design for estimating the unknown
vector of parameters $\boldsymbol{\theta}$ in the proportional hazard rate and
proportional reverse hazard rate models. We examine both maximum likelihood
(ML) and method of moments (MM) methods and investigate the relative precision
of our proposed RNS-based estimators compared with those based on simple random
sampling (SRS). We introduce four types of RNS-based data as well as necessary
EM algorithms for the ML estimation, and evaluate the performance of
corresponding estimators in estimating $\boldsymbol{\theta}$. We show that
there are always values of the design parameters on which RNS-based estimators
are more efficient than those based on SRS. Inference based on imperfect
ranking is also explored and it is shown that the improvement holds even when
the ranking is imperfect. Theoretical results are augmented with numerical
evaluations and a case study.
