مدل لگ نمایی-وایبل معکوس برای سیستم‌های منسجم با مولفه‌های پواسن‌لیندلی بریده شده در صفر
محورهای موضوعی : آمارمرتضی قاسمی چراتی 1 , عزت اله بالوئی جامخانه 2 * , عین اله دیری 3
1 - گروه آمار، واحد قائمشهر، دانشگاه آزاد اسلامی، قائمشهر، ایران
2 - گروه آمار، واحد قائمشهر، دانشگاه آزاد اسلامی، قائمشهر، ایران
3 - گروه آمار، واحد قائمشهر، دانشگاه آزاد اسلامی، قائمشهر، ایران
کلید واژه: r-von-Mises minimum distance, Log Exponential-inverse Weibull, Parallel structure, Zero-truncated, Cramé,
چکیده مقاله :
در این مقاله، دو توزیع جدید، برای یک سیستم منسجم که مجهز به اجزای سری یا موازی است را یشنهاد می‌نماییم. تعداد مولفه‌های سیستم را متغیر تصادفی پواسن‌لیندلی بریده‌شده در صفر در نظر می‌گیریم. توزیع لگ نمایی-وایبل معکوس را در نظر گرفته و آن را به عنوان توزیع پایه سیستم منسجم قرار میدهیم. علاوه بر معرفی دو توزیع منعطف به نام‌های PL-LEIW1 و PL-LEIW2 با تابع شکست با شکل‌های مختلف، ویژگی‌های آماری و مبحث برآوردهای پارامتری و ناپارامتری به طور جامع مورد مطالعه قرار گرفته است. با توجه به تنوع رفتاری در تابع چگالی احتمال و توابع خرابی، این دو توزیع مبتنی بر سیستم‌های سری یا موازی، می‌توانند برای انواع مختلفی از داده‌ها براز‌ش داده شوند. روش‌های برآورد مختلف پارامترها مانند براورد ماکزیمم درستنمایی، براورد حداکثر فاصله حاصلضربی، براورد حداقل مربعات و براورد حداقل فاصله کرامر-ون-میسز از طریق روش‌های شبیه‌سازی مونت کارلو مقایسه می‌شوند و هم‌چنین کاربرد توزیع‌های پیشنهادی با استفاده از دو مجموعه داده واقعی ارزیابی شده است.
In this paper, we proposed two new distributions for a coherent system that is equipped with series or parallel components. The count of components is a zero truncated Poisson Lindley random variable. We considered the Log Exponential-inverse Weibull distribution and set it as the baseline distribution of the coherent system. Besides introducing two flexible distributions, named PL-LEIW1 and PL-LEIW2, with various-shaped failure function, the statistical properties and estimation approaches with the parametric and non-parametric context has been studied, comprehensively. Due to different probability density and failure functions, these two distributions based on series or parallel systems, can be fitted to different types of data sets. Different estimation methods of the parameters as maximum likelihood estimation, maximum product of spacing estimation, least squares estimation and Cramér-von-Mises minimum distance estimation are compared through the Monte Carlo simulation approaches. The applicability of the proposed distributions have been evaluated by two real data sets.
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