زمان مورد انتظار آزمایش‏، برآوردیابی و پیش بینی برای توزیع لیندلی توانی بر اساس داده‌های سانسور شده‌ی فزاینده‌ی نوع دو با برداشت‌های دوجمله‌ای

نوع مقاله : مقاله پژوهشی

نویسندگان

گروه آمار، دانشگاه مازندران، بابلسر، ایران

چکیده

در این مقاله، مسأله‌ی برآوردیابی و پیش‌بینی برای توزیع لیندلی توانی بر اساس داده‌های سانسورشده‌ی فزاینده‌ی نوع دو با برداشت‌های دوجمله‌ای مورد مطالعه قرار می‌گیرد. ابتدا به برآوردیابی پارامترهای توزیع لیندلی توانی به کمک روش‌های درست‌نمایی ماکسیمم و بیزی می‌پردازیم. برآوردیابی بیزی پارامترها بر اساس تابع زیان متقارن توان دوم خطا و تابع زیان نامتقارن آنتروپی عمومی صورت می‌پذیرد. از آن‌جا که برآوردهای بیزی شامل انتگرال‌هایی است که به‌نظر می‌رسند فرم صریحی ندارند، برای تقریب این انتگرال‌ها از الگوریتم متروپولیس-هستینگس بهره می‌گیریم. یک مطالعه‌ی شبیه‌سازی برای بررسی عملکرد برآوردگرهای پارامترها ارائه شده است. در ادامه، مسأله‌ی پیش‌بینی بیزی یک‌نمونه‌ای و دونمونه‌ای مورد بحث قرار می‌گیرد. یک مثال واقعی برای نشان دادن کاربرد روش‌های نظری ارائه‌شده در مقاله ارائه می‌گردد. همچنین، مسأله‌ی زمان مورد انتظار آزمایش با کمک رسم نمودارهایی مورد مطالعه قرار می‌گیرد. مقاله با چندین نتیجه‌‌گیری پایان می‌پذیرد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

‎Expected Experimentation Time, Estimation and Prediction for the Power Lindley Distribution Based on Progressively Type II Censored Data ‎W‎ith Binomial Removals

نویسندگان [English]

  • Esmaeel Azizi
  • S.M.T.K. MirMostafaee
Department of Statistics, University of Mazandaran, Babolsar, Iran
چکیده [English]

In this paper, the problem of estimation and prediction for the power Lindley distribution is studied based on progressively Type-II censored data with binomial removals. First, we work on the estimation of the parameters of the power Lindley distribution with the help of maximum likelihood and Bayesian methods. The Bayesian estimation is done based on the symmetric squared error loss function and the asymmetric general entropy loss function. Since the Bayesian estimates involve integrals that do not seem to have explicit forms, we use the Metropolis-Hastings algorithm to approximate these integrals. A simulation study is presented to evaluate the performance of the estimators of the parameters. In the sequel, the problem of one-sample and two-sample prediction is discussed. A real example is given to illustrate the application of the theoretical methods given in the paper. In addition, the problem of expected experimentation time is studied with the help of drawing plots. The paper ends with several conclusions.

کلیدواژه‌ها [English]

  • Metropolis-Hastings algorithm
  • General entropy loss function
  • Expected experimentation time
  • Delta method
  • Progressive censoring with binomial removals
  • Simulation
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