خانواده جدید G*Q-لگاریتمی: ویژگی‌ها، رویکردهای برآورد و کاربردها
محورهای موضوعی : آمارآرزو امیرزادی 1 , عزت اله بالوئی جامخانه 2 , عین اله دیری 3
1 - گروه آمار، واحد قائمشهر، دانشگاه آزاد اسلامي، قائمشهر، ايران
2 - گروه آمار، واحد قائمشهر، دانشگاه آزاد اسلامي، قائمشهر، ايران
3 - گروه آمار، واحد قائمشهر، دانشگاه آزاد اسلامي، قائمشهر، ايران
کلید واژه: Logarithmic transformation, Reliability function, Importance sampling, E-Bayesian estimator, Life time,
چکیده مقاله :
در این مقاله، به معرفی خانواده جدیدی از توزیع‌های طول عمر به نام خانواده G*Q-لگاریتمی، پرداخته و با استفاده از رویکردهای ماکزیمم درستنمایی، بیز و E-بیز، برآورد پارامترهای خانواده جدید و همچنین آنالیز تابع قابلیت اطمینان متناظر آن را به دست می‌آوریم. علاوه بر این، برخی ویژگی‌های آماری مانند توابع گشتاور غیرمرکزی، گشتاور ناکامل، مولد گشتاورها و تابع چندکی این خانواده را بررسی و با در نظر گرفتن توزیع پایه وایبل معکوس، دو زیرمدل از این خانواده به نام های وایبل معکوس نمایی-لگاریتمی و وایبل معکوس توانی-لگاریتمی را معرفی و ویژگی‌های آماری و برآورد پارامترهای دو مدل جدید معرفی‌شده را ارائه می‌نماییم. در ادامه، با استفاده از رویکرد شبیه‌سازی مونت‌کارلو، روش‌های برآوردیابی را مقایسه می‌نماییم. برتری خانواده جدید معرفی‌شده، در برازش داده‌های واقعی، بر برخی توزیع‌های کلاسیک مانند گاما، وایبل، پارتو، گومپرتز، لیندلی، بور نوع XII ، وایبل معکوس، مارشال الکین-وایبل و وایبل نمایی شده نیز بررسی و گزارش شده است.
In this paper, we introduce a new family of lifetime distributions called the G*Q-Logarithmic family and using the maximum likelihood, Bayesian and E-Bayesian approaches, obtain the estimation of the parameters of the new family as well as analyze the corresponding reliability function. In addition, check some statistical properties such as non-central moment, incomplete moment, moment generating and quantile functions of this family and by considering the inverse Weibull baseline distribution, introduce two sub models of this family called exponential inverse Weibull-logarithmic and power inverse Weibull-logarithmic and represent the statistical properties and parameter estimations of the two new introduced models. In the following, we compare the estimation methods using the Monte Carlo simulation approach. The superiority of the new introduced family to fit real data, with some classical distributions such as gamma, Weibull , Pareto, Gompertz, Lindley, Burr XII type, inverse Weibull, Weibull Mashall-Olkin and exponentiated Weibull has also been investigated and reported.
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