If NPMLE is TRUE, and NPMLE.method is "Wang" ,
empirical distributions are plotted
in cdf using either the constrained Newton method (Wang, 2008)
or the hierarchical constrained Newton method (Wang, 2013)
to compute the overall empirical cdf curve.
If NPMLE is TRUE, and NPMLE.method is "Turnbull.intervals" ,
empirical are plotted
in cdf using the EM approach of Turnbull (Turnbull, 1974).
In those two cases, grey rectangles represent areas
where the empirical distribution function is not unique. In cases
where a theoretical distribution is specified, two goodness-of-fit plots
are also provided, a Q-Q plot (plot of the quantiles of the theoretical fitted
distribution (x-axis) against the empirical quantiles of the data) and a P-P plot
(i.e. for each value of the data set, plot of the cumulative density function
of the fitted distribution (x-axis) against the empirical cumulative density function
(y-axis)). Grey rectangles in a Q-Q plot or a P-P plot also represent areas of
non uniqueness of empirical quantiles or probabilities, directly derived from
non uniqueness areas of the empirical cumulative distribution.
If NPMLE is TRUE, and NPMLE.method is "Turnbull.middlepoints",
empirical and, if specified, theoretical distributions are plotted
in cdf using the EM approach of Turnbull (Turnbull, 1974)
to compute the overall
empirical cdf curve, with confidence intervals if Turnbull.confint is TRUE,
by calls to functions survfit and plot.survfit from the
survival package.
If NPMLE is FALSE empirical and, if specified, theoretical distributions
are plotted in cdf, with data directly reported as segments for interval,
left and right censored data,
and as points for non-censored data. Before plotting, observations are ordered and a rank r
is associated to each of them. Left censored observations are ordered
first, by their right bounds. Interval censored and non censored observations
are then ordered by their mid-points and, at last, right censored observations are
ordered by their left bounds. If leftNA (resp. rightNA) is finite,
left censored (resp. right censored) observations are considered as interval censored
observations and ordered by mid-points with non-censored and interval censored data.
It is sometimes necessary to fix rightNA or leftNA to a realistic
extreme value, even if not exactly known, to obtain a reasonable global ranking of
observations. After ranking, each of the n observations is plotted as a point (one x-value)
or a segment (an interval of possible x-values),
with an y-value equal to r/n, r being the rank of each observation in the global ordering
previously described. This second method may be interesting but
is certainly less rigorous than the other methods
that should be prefered.