Geometry of the \(q\)-exponential distribution with dependent competing risks and accelerated life testing. (English) Zbl 1400.62230
Summary: In the information geometry suggested by S. I. Amari et al. [Differential geometry in statistical inference. Hayward, CA: Institute of Mathematical Statistics (1987; Zbl 0694.62001)], a parametric statistical model can be regarded as a differentiable manifold with the parameter space as a coordinate system. Note that the \(q\)-exponential distribution plays an important role in Tsallis statistics (see [C. Tsallis, Introduction to nonextensive statistical mechanics. Approaching a complex world. Berlin: Springer (2009; Zbl 1172.82004)]), this paper investigates the geometry of the \(q\)-exponential distribution with dependent competing risks and accelerated life testing (ALT). A copula function based on the \(q\)-exponential function, which can be considered as the generalized Gumbel copula, is discussed to illustrate the structure of the dependent random variable. Employing two iterative algorithms, simulation results are given to compare the performance of estimations and levels of association under different hybrid progressively censoring schemes (HPCSs).
MSC:
| 62N05 | Reliability and life testing |
| 53B05 | Linear and affine connections |
| 62N01 | Censored data models |
Keywords:
geometry; \(Q\)-exponential distribution; dependent competing risks; accelerated life testing; copula function; predictionReferences:
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