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Mathematics: EXTENDED GENERALIZED GAMMA DISTRIBUTION

 

EXTENDED GENERALIZED GAMMA DISTRIBUTION

Bachioua Lehcene , Shawki Shaker Hussain*

Department of Mathematics, College of science, Bejaia University. Algeria

*Department of Mathematics, College of Science, University of Baghdad. Baghdad-Iraq

Abstract

New 6-parameters extended form of the Kobayashi's generalized gamma function is defined, several of its properties and recurrence formulas are derived. Based on this new function we introduce a new 6-parameters with a model function extended generalized gamma distribution. Many new distributions are shown to be particular cases of this suggested distribution, including some familiar known distributions. In terms of the model function statistical properties; reliability and hazard functions, and estimation of some parameters of the distribution are studied. Also, the form of the distribution is considered under various forms of the model function.

We believe that this new distribution model is reasonable for accommodate multi various applications, since it have wide variety of shapes. Especially, for the life distribution of a component where the presence of the displacement and intensity parameters is vitally important.

Keywords: Generalized gamma function, generalized gamma distribution, Displacement and intensity parameters, Moments and maximum likelihood methods,

الخلاصة

يهدف هذا البحث الى اقتراح انموذج توزع جديد بدلالة ست معلمات و دالة انموذج يمكن بحد ذاتها صياغتها بدلالة معلمات اخرى و و يطلق على هذا الانموذج انموذج توزع كاما المعمم بالتمدد . يعبر هذا الانموذج عن الكثير من نماذج التوزعات المستمرة في حالاته الخاصة مما يسمح بتمثيل العديد من الظواهر المختلفة  ,خصوصاً في حقل المعولية حيث تشكل معلمتي الازاحة و الشدة اهمية كبرى .و تم دراسة عدد من الخصائص و المميزات النضرية لهذا التوزع , و تم كذلك دراسة دوال المعولية و الاخفاق و سبل تخمين معالم هذا الانموذج.



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