A Modified Method For Bayesian Prediction Of Future Order Statistics From Generalized Power Function - Omar, Almutairi Aned (2015)

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Statistik Bayesian adalah kaedah statistik yang digunakan secara meluas dalam pelbagai bidang seperti perubatan, sains sosial dan ekonomi. Ramalan Bayesian adalah salah satu kaedah statistik Bayesian. Ia bekerja dengan pelbagai kaedah. Kajian ini turut membincangkan tiga kaedah ramalan Bayesian. Terdapat satu sampel, dua sampel dan sampel pelbagai ramalan. Tiga kaedah bertindak balas terhadap motivasi praktikal yang memerlukan data sampel kurang, dalam kebanyakan kajian statistik digunakan. Oleh itu, sampel yang akan datang adalah istilah yang penting dalam tesis ini. Pendekatan Bayesian menggunakan ramalan untuk statistik tertib masa depan berdasarkan data tertib yang diperhatikan dan fungsi ketumpatan ramalan memberi selang ramalan Bayesian untuk statistik tertib masa depan. Taburan fungsi kuasa teritlak piawai adalah dasar untuk tiga kaedah dengan menggunakan teori Bayes untuk mencapai had rendah dan had atas yang sempit bagi selang ramalan Bayesian 95% dan selang ramalan Bayesian 99%. Bayesian statistics is a statistical method that is widely used in many fields, including medicine, social and applied sciences. These fields occasionally have little or limited information about their populations. Therefore, using new techniques that require fewer samples while providing the same quality as the case of available samples is necessary. Bayesian prediction is a commonly used tool in Bayesian statistics. This study modifies three Bayesian prediction methods: one-, two- and multi-sample predictions. Bayesian prediction modified method does not require the many samples. Therefore, a future sample is a significant term in this thesis. Our Bayesian prediction modified method used a prediction for the future order statistics based on the observed ordered data, and predictive densities provided the Bayesian prediction intervals for the future order statistics. The standard generalized power function distribution serves as the basis for the three modified methods by applying Bayes' theory to achieve close lower and upper limits for the 95% and 99% Bayesian prediction intervals.