Modeling without Data Using Expert Opinion - Elementary Latin | LATIN 1, Exams of Latin language

Download Modeling without Data Using Expert Opinion - Elementary Latin | LATIN 1 and more Exams Latin language in PDF only on Docsity! Package ‘expert’ April 17, 2009 Type Package Title Modeling without data using expert opinion Version 1.0-0 Date 2008-09-01 Author Mathieu Pigeon, Michel Jacques, Vincent Goulet Maintainer Mathieu Pigeon <mathieu.pigeon.3@ulaval.ca> Description Expert opinion (or judgment) is a body of techniques to estimate the distribution of a random variable when data is scarce or unavailable. Opinions on the quantiles of the distribution are sought from experts in the field and aggregated into a final estimate. The package supports aggregation by means of the Cooke, Mendel-Sheridan and predefined weights models. Depends R (>= 2.6.0), stats License GPL (>= 2) Encoding latin1 LazyLoad yes LazyData yes ZipData yes Repository CRAN Date/Publication 2008-10-02 12:18:55 R topics documented: cdf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 expert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 hist.expert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 mean.expert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 ogive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 quantile.expert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Index 12 1 2 cdf cdf Expert Aggregated Cumulative Distribution Function Description Compute or plot the cumulative distribution function for objects of class "expert". Usage cdf(x, ...) ## S3 method for class 'cdf': print(x, digits = getOption("digits") - 2, ...) ## S3 method for class 'cdf': knots(Fn, ...) ## S3 method for class 'cdf': plot(x, ..., ylab = "F(x)", verticals = FALSE, col.01line = "gray70") Arguments x an object of class "expert"; for the methods, an object of class "cdf", typi- cally. digits number of significant digits to use, see print. Fn an R object inheriting from "cdf". ... arguments to be passed to subsequent methods, e.g. plot.stepfun for the plot method. ylab label for the y axis. verticals see plot.stepfun. col.01line numeric or character specifying the color of the horizontal lines at y = 0 and 1, see colors. Details The function builds the expert aggregated cumulative distribution function corresponding to the results of expert. The function plot.cdf which implements the plot method for cdf objects, is implemented via a call to plot.stepfun; see its documentation. Value For cdf, a function of class "cdf", inheriting from the "function" class. hist.expert 5 In addition, for method = "cooke", a component alpha containing the confidence level: ei- ther the value given in argument to the function or the optimized value. There are methods available to represent (print), plot (plot), compute quantiles (quantile), summarize (summary) and compute the mean (mean) of "expert" objects. References Cooke, R. (1991), Expert in Uncertainty, Oxford University Press. Mendel, M. and Sheridan, T. (1989), Filtering information from human experts, IEEE Transactions on Systems, Man and Cybernetics, 36, 6–16. Pigeon, M. (2008), Utilisation d’avis d’experts en actuariat, M.Sc. thesis, Université Laval. Examples ## An example with three experts (E1, E2, E3), two seed variables ## (A1, A2) and three quantiles (10th, 50th and 90th). x <- list(E1 <- list(A1 <- c(0.14, 0.22, 0.28), A2 <- c(130000, 150000, 200000), X <- c(350000, 400000, 525000)), E2 <- list(A1 <- c(0.2, 0.3, 0.4), A2 <- c(165000, 205000, 250000), X <- c(550000, 600000, 650000)), E3 <- list(A1 <- c(0.2, 0.4, 0.52), A2 <- c(200000, 400000, 500000), X <- c(625000, 700000, 800000))) probs <- c(0.1, 0.5, 0.9) true.seed <- c(0.27, 210000) ## Cooke model expert(x, "cooke", probs, true.seed, alpha = 0.03) # fixed alpha expert(x, "cooke", probs, true.seed) # optimized alpha ## Mendel-Sheridan model fit <- expert(x, "ms", probs, true.seed) fit # print method summary(fit) # more information ## Predefined weights model expert(x, "weights", probs, true.seed) # equal weights expert(x, "weights", probs, true.seed, w = c(0.25, 0.5, 0.25)) hist.expert Histogram of the Expert Aggregated Distribution Description This method for the generic function hist is mainly useful to plot the histogram of objects of class "expert". If plot = FALSE, the resulting object of class "histogram" is returned for compatibility with hist.default, but does not contain much information not already in x. 6 hist.expert Usage ## S3 method for class 'expert': hist(x, freq = NULL, probability = !freq, density = NULL, angle = 45, col = NULL, border = NULL, main = paste("Histogram of" , xname), xlim = NULL, ylim = NULL, xlab = "x", ylab = expression(f(x)), axes = TRUE, plot = TRUE, labels = FALSE, ...) Arguments x an object of class "expert" freq logical; if TRUE, the histogram graphic is a representation of frequencies, the counts component of the result; if FALSE, probability densities, component density, are plotted (so that the histogram has a total area of one). Defaults to TRUE iff group boundaries are equidistant (and probability is not spec- ified). probability an alias for !freq, for S compatibility. density the density of shading lines, in lines per inch. The default value of NULL means that no shading lines are drawn. Non-positive values of density also inhibit the drawing of shading lines. angle the slope of shading lines, given as an angle in degrees (counter-clockwise). col a colour to be used to fill the bars. The default of NULL yields unfilled bars. border the color of the border around the bars. The default is to use the standard fore- ground color. main, xlab, ylab these arguments to title have useful defaults here. xlim, ylim the range of x and y values with sensible defaults. Note that xlim is not used to define the histogram (breaks), but only for plotting (when plot = TRUE). axes logical. If TRUE (default), axes are draw if the plot is drawn. plot logical. If TRUE (default), a histogram is plotted, otherwise a list of breaks and counts is returned. labels logical or character. Additionally draw labels on top of bars, if not FALSE; see plot.histogram. ... further graphical parameters passed to plot.histogram and their to title and axis (if plot=TRUE). Value An object of class "histogram" which is a list with components: breaks the r + 1 group boundaries. counts r integers; the frequency within each group. density the relative frequencies within each group nj/n, where nj = counts[j]. intensities same as density. Deprecated, but retained for compatibility. mean.expert 7 mids the r group midpoints. xname a character string with the actual x argument name. equidist logical, indicating if the distances between breaks are all the same. Note The resulting value does not depend on the values of the arguments freq (or probability) or plot. This is intentionally different from S. References Klugman, S. A., Panjer, H. H. and Willmot, G. E. (1998), Loss Models, From Data to Decisions, Wiley. See Also hist and hist.default for histograms of individual data and fancy examples. Examples x <- list(E1 <- list(A1 <- c(0.14, 0.22, 0.28), A2 <- c(130000, 150000, 200000), X <- c(350000, 400000, 525000)), E2 <- list(A1 <- c(0.2, 0.3, 0.4), A2 <- c(165000, 205000, 250000), X <- c(550000, 600000, 650000)), E3 <- list(A1 <- c(0.2, 0.4, 0.52), A2 <- c(200000, 400000, 500000), X <- c(625000, 700000, 800000))) probs <- c(0.1, 0.5, 0.9) true.seed <- c(0.27, 210000) fit <- expert(x, "cooke", probs, true.seed, 0.03) hist(fit) mean.expert Arithmetic Mean of the Expert Aggregated Distribution Description Mean of objects of class "expert". Usage ## S3 method for class 'expert': mean(x, ...) 10 quantile.expert Examples x <- list(E1 <- list(A1 <- c(0.14, 0.22, 0.28), A2 <- c(130000, 150000, 200000), X <- c(350000, 400000, 525000)), E2 <- list(A1 <- c(0.2, 0.3, 0.4), A2 <- c(165000, 205000, 250000), X <- c(550000, 600000, 650000)), E3 <- list(A1 <- c(0.2, 0.4, 0.52), A2 <- c(200000, 400000, 500000), X <- c(625000, 700000, 800000))) probs <- c(0.1, 0.5, 0.9) true.seed <- c(0.27, 210000) fit <- expert(x, "cooke", probs, true.seed, 0.03) Fn <- ogive(fit) Fn knots(Fn) # the group boundaries Fn(knots(Fn)) # true values of the empirical cdf Fn(c(80, 200, 2000)) # linear interpolations plot(Fn) quantile.expert Quantiles of the Expert Aggregated Distribution Description Quantile for objects of class "expert". Usage ## S3 method for class 'expert': quantile(x, probs = seq(0, 1, 0.25), smooth = FALSE, names = TRUE, ...) Arguments x an object of class "expert". probs numeric vector of probabilities with values in [0, 1). smooth logical; when TRUE and x is a step function, quantiles are linearly interpolated between knots. names logical; if true, the result has a names attribute. Set to FALSE for speedup with many probs. ... further arguments passed to or from other methods. quantile.expert 11 Details The quantiles are taken directly from the cumulative distribution function defined in x. Linear interpolation is available for step functions. Value A numeric vector, named if names is TRUE. See Also expert Examples x <- list(E1 <- list(A1 <- c(0.14, 0.22, 0.28), A2 <- c(130000, 150000, 200000), X <- c(350000, 400000, 525000)), E2 <- list(A1 <- c(0.2, 0.3, 0.4), A2 <- c(165000, 205000, 250000), X <- c(550000, 600000, 650000)), E3 <- list(A1 <- c(0.2, 0.4, 0.52), A2 <- c(200000, 400000, 500000), X <- c(625000, 700000, 800000))) probs <- c(0.1, 0.5, 0.9) true.seed <- c(0.27, 210000) fit <- expert(x, "cooke", probs, true.seed, 0.03) quantile(fit) # default probs quantile(fit, probs = c(0.9, 0.95, 0.99)) # right tail Index ∗Topic distribution expert, 3 hist.expert, 5 ∗Topic dplot cdf, 2 hist.expert, 5 ogive, 8 ∗Topic hplot cdf, 2 hist.expert, 5 ogive, 8 ∗Topic models expert, 3 ∗Topic univar mean.expert, 7 quantile.expert, 10 approxfun, 9 axis, 6 cdf, 2, 9 colors, 2 ecdf, 3 expert, 2, 3, 3, 8, 9, 11 format, 4 function, 2, 9 hist, 5, 7 hist.default, 5, 7 hist.expert, 5 knots.cdf (cdf), 2 knots.ogive (ogive), 8 mean.expert, 7 ogive, 3, 8 plot, 2 plot.cdf (cdf), 2 plot.histogram, 6 plot.ogive (ogive), 8 plot.stepfun, 2 print, 2, 9 print.cdf (cdf), 2 print.expert (expert), 3 print.ogive (ogive), 8 print.summary.expert (expert), 3 quantile.expert, 10 stepfun, 3, 9 summary.expert (expert), 3 title, 6 12