نموذج انحدار بواسون الموسع مزدوج البتر ENDPOINT-INFLATED DOUBLE TRUNCATED POISSON MODEL

نوع المستند : المقالة الأصلية

المؤلفون

Statistics Department, Faculty of Commerce, AL-Azhar University (Girls' Branch), Cairo, Egypt

المستخلص

تم اقتراح توزيع بواسون الموسع مزدوج البتر Distribution) Endpoint-Inflated Double Truncated Poisson)  وذلك لتمثيل متغير عشوائي يأخذ قيم لبيانات Count Data)) والتي تحتوي على عدد كبير من الأصفار(Left Endpoint) بالإضافة الي وجود قيمة أخرى ذات تكرار كبير أيضًا Right Endpoint)) مقارنةً بالقيم الأخرى للبيانات، والتي لا يمكن تفسيرها بواسطة الفروض الأساسية لتوزيع بواسون. يعد توزيع بواسون الموسع مزدوج البتر خليطا من ثلاث مكونات، قيمة الاحتمال عند النقطة (صفر)، وقيمة الاحتمال عند النقطة (m) ، وباقي القيم التي يأخذها المتغير العشوائي يمثلها توزيع بواسون مزدوج البتر  .( Double Truncated Poisson Distribution) تمت مناقشة بعض خصائص التوزيع. تم استخدام كل من طريقة الإمكان الأكبر وطريقة العزوم للحصول على المقدرات وفترات الثقة لمعالم التوزيع. تم اقتراح نموذج انحدار بواسون الموسع مزدوج البتر (Endpoint-Inflated Double Truncated Poisson Model). تم إجراء دراسة محاكاة  (Simulation Study) لتقييم أداء الطرق المقترحة. تم تحليل مجموعة بيانات حقيقية لتوضيح كيف يمكن تطبيق الأساليب عمليًا.
Abstract
This article is concerned with Endpoint-Inflated Double Truncated Poisson distribution which is developed for modeling count data with excessive zeros (left-endpoint) and excessive right-endpoint compared with other observations of the data. This method for modeling such data is based on an assumption that the random variable is generated from a mixture distribution of three components. The probability when the value for the response variable is zero, the probability when the value for the response variable is , and the other counts are defined by Double Truncated Poisson distribution. Some of its main properties are discussed. The maximum likelihood and moment methods of estimations are utilized to derive point estimators and confidence intervals for the parameters. Regression model based on the distribution is proposed and the corresponding computational procedures are introduced. A simulation study is conducted to evaluate the performance of the proposed methods. A real data set is analyzed to demonstrate how the methods can be applied in practice. 
 

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