require(actuar) require(fitdistrplus) n <- 1e4 truescale <- 100 trueshape1 <- pi if(FALSE) { plot(ecdf(rburr(n, trueshape1, 2, scale=truescale))) lines(ecdf(1/rinvburr(n, trueshape1, 2, scale=1/truescale)), col="red") curve(pburr(x, trueshape1, 2, scale=truescale), from=0, to=5*truescale) curve(pinvburr(1/x, trueshape1, 2, scale=1/truescale, lower=FALSE), add=TRUE, col="red") } z <- rburr(n, trueshape1, 2, scale=truescale) y <- 1/z fit_y_IB <- fitdist(y, "invburr") mytitle <- paste("fitted Inv. Burr", paste(signif(coef(fit_y_IB), 3), collapse= ", ")) myleg <- paste("theo. Inv. Burr", paste(signif(c(trueshape1, 2, 1/truescale), 3), collapse= ", ")) cdfcomp(fit_y_IB, xlogscale = TRUE, do.points = FALSE, addlegend = FALSE, main=mytitle) curve(pinvburr(x, trueshape1, 2, scale=1/truescale), add=TRUE, col="green") legend("topleft", lty=1, col=c("black", "red", "green"), c("empirical", "fitted", myleg)) y <- rinvburr(n, trueshape1, 2, scale=1/truescale) fit_y_IB <- fitdist(y, "invburr") mytitle <- paste("fitted Inv. Burr", paste(signif(coef(fit_y_IB), 3), collapse= ", ")) myleg <- paste("theo. Inv. Burr", paste(signif(c(trueshape1, 2, 1/truescale), 3), collapse= ", ")) cdfcomp(fit_y_IB, xlogscale = TRUE, do.points = FALSE, addlegend = FALSE, main=mytitle) curve(pinvburr(x, trueshape1, 2, scale=1/truescale), add=TRUE, col="green") legend("topleft", lty=1, col=c("black", "red", "green"), c("empirical", "fitted", myleg))