The log-normal QQ-plot adapted for right censoring is given by
$$( \Phi^{-1}(F_{km}(Z_{j,n})), \log(Z_{j,n}) )$$
for \(j=1,\ldots,n-1,\)
with \(Z_{i,n}\) the \(i\)-th order statistic of the data, \(\Phi^{-1}\) the quantile function of the standard normal distribution and \(F_{km}\) the Kaplan-Meier estimator for the CDF.
Hence, it has the same empirical quantiles as an ordinary log-normal QQ-plot but replaces the theoretical quantiles \( \Phi^{-1}(j/(n+1))\) by \(\Phi^{-1}(F_{km}(Z_{j,n}))\).
This QQ-plot is only suitable for right censored data.
In Beirlant et al. (2007), only a Pareto QQ-plot adapted for right-censored data is proposed. This QQ-plot is constructed using the same ideas, but is not described in the paper.