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BvCh 0.1.0

First release.

Models

• BvCh — Marshall-Olkin type Bivariate Chen distribution. Probability density (dbvch), survival function (sbvch), hazard function (hbvch) and random generation (rbvch), plus the two components of the mixture representation (dbvch_ac, dbvch_sing).
• BEC — Bivariate Extended Chen distribution: dbec, sbec, hbec, rbec, and the componentwise hazard gradients hbec1 and hbec2.
• IFGM-Chen — Bivariate Inverse FGM Chen distribution built from the Inverse FGM copula and Chen marginals: relifgmchen, difgmchen, hifgmchen, rifgmchen, together with the copula itself (cifgm, cifgmdens, rifgm) and its dependence measures (tau_ifgm, rho_ifgm).

Univariate building blocks

• Univariate Chen density, distribution, quantile, survival, hazard, hazard-rate-average, conditional reliability and random generation are taken from reliaR rather than re-implemented.
• The univariate Extended Chen distribution, which reliaR does not provide, is implemented here (sech, hech, dech, pech, qech, rech).

Estimation, comparison and graphics

• Maximum likelihood estimation: fitbvch, fitbec, fitifgmchen, with standard errors from the numerical Hessian, and logLik_bvch, logLik_bec, logLik_ifgmchen exported for direct use.
• compare_models tabulates −log L, AIC and BIC; ksfit_bvch performs Kolmogorov-Smirnov goodness-of-fit tests for the three marginals.
• Base-graphics surface and contour plots: plot_surface_bvch, plot_surface_bec, plot_reliability_ifgmchen, plot_contour_bvch.

Notes

• BvCh::rchen draws reliaR::qchen(runif(n), beta, lambda) rather than calling reliaR::rchen, because in reliaR 0.2 that function disagrees with the package’s own distribution function (Kolmogorov-Smirnov distance about 0.38 at beta = 1.5, lambda = 2, growing to about 0.85 at beta = 2.5, and correct only when beta = 1). See ?chen.
• hbvch implements the hazard as f/S; on the diagonal this reproduces the source formula h0(z) = alpha3 * beta * z^(beta-1) * exp(z^beta) exactly.
• With the Inverse FGM copula formula as written in the source document, tau_ifgm and rho_ifgm are non-positive for gamma, omega >= 0 (tau = -0.0699, rho = -0.1049 at gamma = 0.6, omega = 0.4). The source document quotes a positive tau = 0.156 for the same parameters, which is inconsistent with the copula it also quotes. The formula has been implemented as given; see ?cifgm.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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