International Journal of Mathematics Trends and Technology
Volume 60 | Number 4 | Year 2018 | Article Id. IJMTT-V60P538 | DOI : https://doi.org/10.14445/22315373/IJMTT-V60P538
In this article a new way of statistical updating prediction and measuring behavior in the field of animal population dynamics and ecological data science is studied and examined on the species richness model. To estimate the size of closed population, with individual heterogeneity in detection probability, we have introduced and used generalized binomial model with five parameters GBM(n,p,π,ρ,τ) [[1] Al-Saleh at el. (2016)], as an alternative model to the standard Binomial model SBM(n,p). The generalized model is developed by introducing new parameters called indicator parameters. The main advantage of an indicator parameter, is that, it will equip the new generalized model accession, more approaches, and options in statistical estimation for close fitting and measuring behavior of the data. To help with the examination of the data more precisely, we also consider a new mixture unit interval type prior on (0,1) with two parameters UITP(α,β), as an alternative model to the uniform prior on (0,1). To be a contrivance, and intermediary updating prediction model to exiting model [[2] Royle and Dorazio (2008), Chapter 6], and reproduce more effective, generalized, and propagated model of particular importance for species richness populations, using capture–recapture model. The estimate of the total population size could be affected by the selection of the model suggested to fit the data. Therefore, we propose an expanded, generalized, and extended model with the advantage that the model parameters can be estimated using Bayesian methodology which serves as a subtle resource for model identification and classification. An illustration is provided using species richness model with the application to bird breeding survey (BBS) data set. The generalized posterior summaries using Markov Chain Monte Carlo (MCMC) Gibbs sampling approach, are presented for the new models. The study of the parameters of the new models would help the users to have more clarity and understanding about the role of the existing model. It is found that proposed new models is more resilience, litheness, and is fully adaptive to the available data and gives animal ecologist another option for modelling the data.
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Jamal A. Al-Saleh, Satish K. Agarwal, "Bird breeding Avian Data: Bayesian Statistical Updating Prediction for the Size of Closed Population on the Species Richness Model Using Generalized Binomial Model with New Mixture Unit Interval Type Prior for Animal Ecology," International Journal of Mathematics Trends and Technology (IJMTT), vol. 60, no. 4, pp. 254-262, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V60P538
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