Bayesian estimation of the mixture of generalized exponential distribution: a versatile lifetime model in industrial processes

Abstract

Constructing a flexible parametric classes of probability distributions is most popular approach in Bayesian analysis for the last few decades. This study is planned in the same direction for two components’ mixture of generalized exponential (GE) probability distribution by considering heterogeneous population from industry. We have considered censored sample environment due to its popularity in reliability theory. In addition, we have worked out expressions for the maximum likelihood estimates along with their variances and constructed components of the information matrix. To examine the performance of these estimators, we have evaluated their properties for different sample sizes, censoring rates, proportions of the component of mixture, and a variety of loss functions (LFs). The Bayes estimates are evaluated under squared error, entropy, squared logarithmic, and precautionary LFs. Hazard rate of GE distribution graphically and numerically compared with mixture of other life-time distributions. To highlight the practical significance, we have included an illustrative application example based on a real-life data.

過去幾十年 ， 使用貝氏分析建構一個具有彈性的機率分配參數類別是最普遍的方法。 這項研究被計畫朝同一方向 ， 是由於考慮企業異質母體下的混合廣義指數機率分配的兩個要素 ， 我們也考慮設限的樣本環境 ， 因其在可靠理論中相當地普及。 此外我們已經得到最大概似估計量及其變異和資訊矩陣的構成要素的表達方式。 為了檢驗這些估計量的績效 ， 我們會評估不同樣本大小 、 對稱熵率、 元素混合的比率和損失函數變異這些權重。 貝氏估計值是以平方差、 對稱熵、 平方對數和預防損失函數而評估出來的 ， 而廣義指數分配的失敗率圖形和數值與其他壽命時間分配混合比較。 為了強調其可行性 ， 我們以真實的實行數據舉例說明。

(*聯絡人 ： [email protected])

Keywords:

• entropy loss function
• generalized exponential distribution
• hazard rate of mixture distribution
• precautionary loss function
• squared error loss function
• squared logarithmic loss function

Keywords:

• 關鍵字 ： 對稱熵損失函數 ； 廣義指數分配 ； 損害率混合分配 ； 預防損失函數;平方誤損失函數;平方對數損失函數

Acknowledgements

The authors would like to thank the anonymous referees and especially to the editor of Journal of the Chinese Institute of Industrial Engineers for their potential comment for the improvement of the article.

Notes

(*聯絡人 ： [email protected])