Sankhy¯ a A : The Indian Journal of Statistics https://doi.org/10.1007/s13171-018-00159-8 c  2019, Indian Statistical Institute Parametric Inference Using Nomination Sampling with an Application to Mercury Contamination in Fish Mohammad Nourmohammadi Statistical Research and Training Center of Iran, Tehran, Iran Mohammad Jafari Jozani and Brad C. Johnson University of Manitoba, Winnipeg, Canada Abstract Randomized nomination sampling (RNS) is a rank-based sampling technique which has been shown to be effective in several nonparametric studies involv- ing environmental, agricultural, medical and ecological applications. In this paper, we investigate parametric inference using RNS design for estimating an unknown vector of parameters θ in some parametric families of distribu- tions. We examine both maximum likelihood (ML) and method of moments (MM) approaches. We introduce four types of RNS-based data as well as necessary EM algorithms for the ML estimation under each data type, and evaluate the performance of corresponding estimators in estimating θ com- pared with those based on simple random sampling (SRS). Our results can address many parametric inference problems in reliability theory, sport ana- lytics, fisheries, etc. Theoretical results are augmented with numerical evalu- ations, where we also study inference based on imperfect ranking. We apply our methods to a real data problem in order to study the distribution of the mercury contamination in fish body using RNS designs. AMS (2000) subject classification. Primary 62G05; Secondary 62D05. Keywords and phrases. Randomized nomination sampling, Method of moments, Maximum likelihood, Modified maximum likelihood, EM algorithm 1 Introduction Randomized nomination sampling (RNS) is a rank-based sampling scheme. Rank-based sampling schemes are data collection techniques which utilize the advantage of additional information available in the population to pro- vide an artificially stratified sample with more structure. Providing more