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Mixture Model Analysis of Partially Rank-Ordered Set Samples: Age Groups of Fish from Length-Frequency Data

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  • Armin Hatefi
  • Mohammad Jafari Jozani
  • Omer Ozturk

Abstract

type="main" xml:id="sjos12140-abs-0001"> We present a novel methodology for estimating the parameters of a finite mixture model (FMM) based on partially rank-ordered set (PROS) sampling and use it in a fishery application. A PROS sampling design first selects a simple random sample of fish and creates partially rank-ordered judgement subsets by dividing units into subsets of prespecified sizes. The final measurements are then obtained from these partially ordered judgement subsets. The traditional expectation–maximization algorithm is not directly applicable for these observations. We propose a suitable expectation–maximization algorithm to estimate the parameters of the FMMs based on PROS samples. We also study the problem of classification of the PROS sample into the components of the FMM. We show that the maximum likelihood estimators based on PROS samples perform substantially better than their simple random sample counterparts even with small samples. The results are used to classify a fish population using the length-frequency data.

Suggested Citation

  • Armin Hatefi & Mohammad Jafari Jozani & Omer Ozturk, 2015. "Mixture Model Analysis of Partially Rank-Ordered Set Samples: Age Groups of Fish from Length-Frequency Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 848-871, September.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:3:p:848-871
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    File URL: http://hdl.handle.net/10.1111/sjos.12140
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    References listed on IDEAS

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    1. Gao, Jinguo & Ozturk, Omer, 2012. "Two sample distribution-free inference based on partially rank-ordered set samples," Statistics & Probability Letters, Elsevier, vol. 82(5), pages 876-884.
    2. Furman, W. David & Lindsay, Bruce G., 1994. "Measuring the relative effectiveness of moment estimators as starting values in maximizing likelihoods," Computational Statistics & Data Analysis, Elsevier, vol. 17(5), pages 493-507, June.
    3. Gang Zheng & Mohammad Al-Saleh, 2002. "Modified Maximum Likelihood Estimators Based on Ranked Set Samples," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(3), pages 641-658, September.
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