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Neyman–Scott process with alpha-skew-normal clusters

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Abstract

The Neyman–Scott processes introduced so far assume a symmetric distribution for the positions of the offspring points and this makes them inappropriate for modelling the skewed and bimodal clustered patterns and is a hindrance in fitting them to data that exhibit skewness or bimodality. In this paper, we apply the bivariate alpha-skew-normal distribution to the locations of the offspring points and introduce a Neyman–Scott process that regulates skewness and bimodality shapes in clustered point patterns. For this process, we obtain closed forms of the pair correlation function and the third-order intensity reweighted product density function and by use of the composite likelihood method, we fit the model to data. To examine the goodness-of-fit of the presented model, we use a statistical test based on the combined global scaled MAD envelopes. The use of the introduced process to model a clustered point pattern is illustrated by application to the locations of a species of trees in a rainforest dataset.

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Acknowledgements

The BCI forest dynamics research project was made possible by National Science Foundation grants to Stephen P. Hubbell: DEB-0640386, DEB-0425651, DEB-0346488, DEB-0129874, DEB-00753102, DEB-9909347, DEB-9615226, DEB-9615226, DEB-9405933, DEB-9221033, DEB-9100058, DEB-8906869, DEB-8605042, DEB-8206992, DEB-7922197, support from the Center for Tropical Forest Science, the Smithsonian Tropical Research Institute, the John D. and Catherine T. MacArthur Foundation, the Mellon Foundation, the Small World Institute Fund, and numerous private individuals, and through the hard work of over 100 people from 10 countries over the past two decades. The plot project is part the Center for Tropical Forest Science, a global network of large-scale demographic tree plots. The authors would like to thank Dr. Mari Myllymäki for useful suggestions regarding the use of \(\mathtt {R}\) package \(\mathtt {GET}\).

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Authors and Affiliations

  1. Department of Statistics, Shahid Beheshti University, Evin, Tehran, Iran

    Nader Najari & Mohammad Q. Vahidi Asl

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  1. Nader Najari
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  2. Mohammad Q. Vahidi Asl
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Correspondence to Nader Najari.

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Handling Editor: Bryan F. J. Manly.

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Najari, N., Vahidi Asl, M.Q. Neyman–Scott process with alpha-skew-normal clusters. Environ Ecol Stat 28, 73–86 (2021). https://doi.org/10.1007/s10651-020-00476-y

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  • DOI: https://doi.org/10.1007/s10651-020-00476-y

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