Parametric and nonparametric inference for the reliability of copula‐based stress‐strength models

Abstract

This paper provides a general treatment of statistical inference for the reliability in copula-based stress-strength models. Most of the current literature is either focused on specific models that yield clean formulas or restricted to estimation and engineering aspects without addressing statistical inference. We present two general frameworks, one parametric, one nonparametric, for the estimation of the reliability. The parametric methodology is presented under the general framework of estimating equations, mostly as a combination of existing methodologies from the fields of multivariate analysis, reliability, and econometrics, with some new results. The nonparametric methodology is a novel application based on an existing bivariate kernel method combined with Monte Carlo estimation of the reliability without specification of the copula or the margins. We present results from a small simulation study designed to assess the robustness of the methods discussed in terms of model misspecification. We used geotechnical data and data from the Brazilian Household Survey to illustrate the proposed methodologies in the estimation of factors of safety and financial fragility.

Solving the geometric reliability index for a case involving multivariate random variables in the original physical space

“…Thus, the joint distribution can be obtained based on the marginal distributions of the variables (not necessarily normal) and the linear correlation matrix. The other commonly used copulas 30 to describe various dependence patterns of random variables, such as Frank, Clayton, and Gumbel, are worth exploring their applicability in the proposed technique.…”

Computation of the Mann–Whitney Effect under Parametric Survival Copula Models

“…Domma & Giordano [47] FGM, Generalized FGM, Frank Burr III, Dagum, Singh-Maddala Gao et al [48] Mixed (Clayton, Gumbel, Frank) Empirical de Andrade et al [49] Clayton, Gumbel, Frank, Gauss, Plackett Weibull, Gamma, Log-normal, Dagum Rathie et al [50] Frank Dagum, Log-Dagum James et al [51] FGM Rayleigh Shang & Yan [52] Clayton Weibull, Kumaraswamy Lima et al [53] Clayton, Frank, Gumbel-Houggard Generalized extreme value, Weibull, gamma…”