Package: gpciLindApproxProgII 0.1.1

gpciLindApproxProgII: Lindley Approximation for Capability Indices under Progressive Censoring

Implements Bayesian parameter and Generalized Process Capability Indices (GPCIs) estimation using the Lindley approximation method (Lindley, 1980 <doi:10.2307/2345271>) under progressive Type-II censored data (Balakrishnan & Aggarwala, 2000 <doi:10.1007/978-1-4612-1334-5>). Evaluates point estimates and posterior expectations for classical and non-normal capability indices, including Cpy (Maiti et al., 2010 <doi:10.1080/16843703.2010.11673233>), Spmk (Dey & Saha, 2019 <doi:10.1007/s41872-019-00081-4>), CpTk (Saha et al., 2019 <doi:10.1007/s13198-019-00789-7>), Cpc (Saha et al., 2022 <doi:10.1080/02664763.2021.1971632>), CNpmc (Alotaibi et al., 2022 <doi:10.1155/2022/3135264>), CNpmkc (Saha et al., 2024 <doi:10.1142/S021853932450013X>), CNpk (Saha et al., 2018 <doi:10.1080/21681015.2018.1437793>), and Vannman's Cp(u,v) family (Vannman, 1995 <doi:10.1111/j.1467-9574.1995.tb01472.x>). Calculates point estimates, bias, mean squared error (MSE), Bayes risk under Linex and squared error loss, Highest Posterior Density (HPD) credible intervals at 90%, 95%, and 99% levels, and Heidelberger and Welch's MCMC convergence diagnostics (Heidelberger & Welch, 1983 <doi:10.1287/opre.31.6.1109>) with convergence probabilities. Accommodates user-defined probability density/mass functions, cumulative distribution functions, and survival functions. Supports progressive parametric and non-parametric bootstrap confidence intervals (Efron, 1987 <doi:10.1080/01621459.1987.10478410>) at 90%, 95%, and 99% significance levels.

Authors:Shikhar Tyagi [aut, cre], Sumit Kumar [aut], Arvind Pandey [aut], Bhupendra Singh [aut], Vrijesh Tripathi [aut]