LL-plot with fitted and empirical survival function
This function plots the logarithm of the empirical survival function (determined using the Empirical CDF (ECDF)) versus the logarithm of the data. Moreover, the logarithm of the fitted survival function of the spliced distribution is added.
SpliceLL(x = sort(X), X, splicefit, plot = TRUE, main = "Splicing LL-plot", ...)
x |
Vector of points to plot the fitted survival function at. By default we plot it at the data points. |
X |
Data used for fitting the distribution. |
splicefit |
A |
plot |
Logical indicating if the splicing LL-plot should be made, default is |
main |
Title for the plot, default is |
... |
Additional arguments for the |
The LL-plot consists of the points
(\log(x_{i,n}), \log(1-\hat{F}(x_{i,n})))
for i=1,…,n with n the length of the data, x_{i,n} the i-th smallest observation and \hat{F} the empirical distribution function. Then, the line
(\log(x), \log(1-\hat{F}_{spliced}(x))),
with \hat{F}_{spliced} the fitted spliced distribution function, is added.
Use SpliceLL_TB
for censored data.
See Reynkens et al. (2017) and Section 4.3.1 in Albrecher et al. (2017) for more details.
A list with following components:
logX |
Vector of the logarithms of the sorted data. |
sll.the |
Vector of the theoretical log-probabilities \log(1-\hat{F}_{spliced}(x)). |
logx |
Vector of the logarithms of the points to plot the fitted survival function at. |
sll.emp |
Vector of the empirical log-probabilities \log(1-\hat{F}(x_{i,n})). |
Tom Reynkens
Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.
Reynkens, T., Verbelen, R., Beirlant, J. and Antonio, K. (2017). "Modelling Censored Losses Using Splicing: a Global Fit Strategy With Mixed Erlang and Extreme Value Distributions". Insurance: Mathematics and Economics, 77, 65–77.
Verbelen, R., Gong, L., Antonio, K., Badescu, A. and Lin, S. (2015). "Fitting Mixtures of Erlangs to Censored and Truncated Data Using the EM Algorithm." Astin Bulletin, 45, 729–758
## Not run: # Pareto random sample X <- rpareto(1000, shape = 2) # Splice ME and Pareto splicefit <- SpliceFitPareto(X, 0.6) x <- seq(0, 20, 0.01) # Plot of spliced CDF plot(x, pSplice(x, splicefit), type="l", xlab="x", ylab="F(x)") # Plot of spliced PDF plot(x, dSplice(x, splicefit), type="l", xlab="x", ylab="f(x)") # Fitted survival function and empirical survival function SpliceECDF(x, X, splicefit) # Log-log plot with empirical survival function and fitted survival function SpliceLL(x, X, splicefit) # PP-plot of empirical survival function and fitted survival function SplicePP(X, splicefit) # PP-plot of empirical survival function and # fitted survival function with log-scales SplicePP(X, splicefit, log=TRUE) # Splicing QQ-plot SpliceQQ(X, splicefit) ## End(Not run)
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