A new class of defective models based on the Marshall-Olkin family of distributions for cure rate modeling

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• 作者：Ricardo Rocha^a ; ^{ricardorocha23@hotmail.com} ; Saralees Nadarajah^b ; Vera Tomazella^a ; Francisco Louzada^c
• 关键词：Defective distributions ; Extended Weibull distribution ; Long-term survivors ; Regression modeling ; Survival analysis
• 刊名：Computational Statistics & Data Analysis
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：107
• 期：Complete
• 页码：48-63
• 全文大小：2001 K
• 卷排序：107

文摘

Defective distributions model cure rates by changing the usual domain of its parameters in a way that their survival functions converge to a value p∈(0,1)p∈(0,1). A new way to generate defective distributions to model cure fractions is proposed. The new way relies on a property derived from the Marshall–Olkin family of distributions. To exemplify this new result we use the extended Weibull distribution and introduce ten new defective distributions. A regression approach for these models is also proposed. Estimation by maximum likelihood is discussed and their asymptotes verified through simulations. Practical use is illustrated by applications to four real data sets.