Surles J G, Padgett W J
Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409, USA.
Lifetime Data Anal. 2001 Jun;7(2):187-200. doi: 10.1023/a:1011352923990.
Inference for R = P(Y < X) is considered when X and Y are independently distributed as scaled Burr type X random variables. Under this model, exact inference procedures for R cannot be found. Hence, based on the expected Fisher information matrix which is derived here, asymptotic inference procedures for R and other general functions of the parameters are developed. A bootstrap method to estimate variance for the maximum likelihood estimators is also discussed. To illustrate these techniques, an example using carbon fiber strength data is given. Simulations to assess the effectiveness of these techniques, as well as other concerns, are presented.
当X和Y作为尺度化布尔类型X随机变量独立分布时，考虑对R = P(Y < X)进行推断。在此模型下，找不到关于R的精确推断程序。因此，基于此处推导的期望Fisher信息矩阵，开发了关于R以及参数的其他一般函数的渐近推断程序。还讨论了一种用于估计最大似然估计量方差的自助法。为说明这些技术，给出了一个使用碳纤维强度数据的示例。还给出了评估这些技术有效性以及其他问题的模拟。
