Plots an empirical distribution for censored data with a theoretical one if specified.
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A dataframe of two columns respectively named
A character string
A named list giving the parameters of the named distribution. This argument may be
omitted only if
the real value of the left bound of left censored observations :
the real value of the right bound of right censored observations :
if TRUE an NPMLE (nonparametric maximum likelihood estimate) technique is
used to estimate the cdf curve of the censored data
and previous arguments
if TRUE confidence intervals will be added to the Turnbull plot.
In that case NPMLE.method is forced to
Three NPMLE techniques are provided,
further graphical arguments passed to other methods. The title of the plot
can be modified using the argument
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.
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.
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
by calls to functions
plot.survfit from the
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
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
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.
Marie-Laure Delignette-Muller and Christophe Dutang.
Turnbull BW (1974), Nonparametric estimation of a survivorship function with doubly censored data. Journal of American Statistical Association, 69, 169-173.
Wang Y (2008), Dimension-reduced nonparametric maximum likelihood computation for interval-censored data. Computational Statistics & Data Analysis, 52, 2388-2402.
Wang Y and Taylor SM (2013), Efficient computation of nonparametric survival functions via a hierarchical mixture formulation. Statistics and Computing, 23, 713-725.
Wang, Y., & Fani, S. (2018), Nonparametric maximum likelihood computation of a U-shaped hazard function. Statistics and Computing, 28(1), 187-200.
Delignette-Muller ML and Dutang C (2015), fitdistrplus: An R Package for Fitting Distributions. Journal of Statistical Software, 64(4), 1-34.
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# (1) Plot of an empirical censored distribution (censored data) as a CDF # using the default Wang method # data(smokedfish) d1 <- as.data.frame(log10(smokedfish)) plotdistcens(d1) # (2) Add the CDF of a normal distribution # plotdistcens(d1, "norm", para=list(mean = -1.6, sd = 1.5)) # (3) Various plots of the same empirical distribution # # default Wang plot with representation of equivalence classess plotdistcens(d1, NPMLE = TRUE, NPMLE.method = "Wang") # same plot but using the Turnbull alorithm from the package survival plotdistcens(d1, NPMLE = TRUE, NPMLE.method = "Wang") # Turnbull plot with middlepoints (as in the package survival) plotdistcens(d1, NPMLE = TRUE, NPMLE.method = "Turnbull.middlepoints") # Turnbull plot with middlepoints and confidence intervals plotdistcens(d1, NPMLE = TRUE, NPMLE.method = "Turnbull.middlepoints", Turnbull.confint = TRUE) # with intervals and points plotdistcens(d1,rightNA=3, NPMLE = FALSE) # with intervals and points # defining a minimum value for left censored values plotdistcens(d1,leftNA=-3, NPMLE = FALSE)
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