# Distribution of the fitted distribution without cut. If observations is a data.frame, it can have 4 columns: A column for the measurements; A column for the lower detection limit; A column for the upper detection limit; A column for the truncated of censored nature of the data. The names of the different columns are in the observations.colname, lower_detection_limit.colname, upper_detection_limit.colname and cut_method.colname. If lower_detection_limit.colname is NULL or if the column does not exist, the data are supposed to not be left-cut and if upper_detection_limit.colname is NULL or if the column does not exist, the data are supposed to not be right-cut. If observations is a vector, then the parameters lower_detection_limit and/or upper_detection_limit must be given. Then cut_method must be also provided. In abservations, -Inf must be used to indicate a value below the lower detection limit and +Inf must be used for a value above the upper detection limit. Be careful: NA is used to represent a missing data and not a value below of above the detection limit. If lower_detection_limit, upper_detection_limit or cut_method are only one value, they are supposed to be used for all the observations. Definitions for censored or truncated distribution vary, and the two terms are sometimes used interchangeably. Let the following data set: 1 1.25 2 4 5 Censoring: some observations will be censored, meaning that we only know that they are below (or above) some bound. This can for instance occur if we measure the concentration of a chemical in a water sample. If the concentration is too low, the laboratory equipment cannot detect the presence of the chemical. It may still be present though, so we only know that the concentration is below the laboratory's detection limit. If the detection limit is 1.5, so that observations that fall below this limit is censored, our example data set would become: <1.5 <1.5 2 4 5; that is, we don't know the actual values of the first two observations, but only that they are smaller than 1.5. Truncation: the process generating the data is such that it only is possible to observe outcomes above (or below) the truncation limit. This can for instance occur if measurements are taken using a detector which only is activated if the signals it detects are above a certain limit. There may be lots of weak incoming signals, but we can never tell using this detector. If the truncation limit is 1.5, our example data set would become: 2 4 5; and we would not know that there in fact were two signals which were not recorded. If n.iter is NULL, no Bayesian MCMC is performed but credible interval will not be available. ```r cutter( observations = stop("Observations must be provided"), observations.colname = "Observations", lower_detection_limit.colname = "LDL", upper_detection_limit.colname = "UDL", cut_method.colname = "Cut", par = NULL, lower_detection_limit = NULL, upper_detection_limit = NULL, cut_method = "censored", distribution = "gamma", n.mixture = 1, n.iter = 5000, n.adapt = 100, debug = FALSE, progress.bar = TRUE, priors = NULL, adaptive = TRUE, session = NULL ) ``` ## Arguments - `observations`: The observations; see description - `observations.colname`: If observations is a data.frame, the name of column with observations - `lower_detection_limit.colname`: If observations is a data.frame, the name of column with lower detection limit - `upper_detection_limit.colname`: If observations is a data.frame, the name of column with upper detection limit - `cut_method.colname`: If observations is a data.frame, the name of column with cut method, being "censored" or "truncated" - `par`: Initial values for parameters of distribution - `lower_detection_limit`: Value for lower detection limit - `upper_detection_limit`: Value for upper detection limit - `cut_method`: Value for cut method, being "censored" or "truncated" - `distribution`: Can be gamma, normal, weibull, lognormal, or generalized.gamma - `n.mixture`: Number of distributions - `n.iter`: Number of iteration for Bayesian MCMC and to estimate the goodness-of-fit - `n.adapt`: Number of burn-in iterations Bayesian MCMC - `debug`: If TRUE, show some information - `progress.bar`: If TRUE, show a progress bar for MCMC - `priors`: A dataframe with priors. - `adaptive`: Should the adaptive methodologie for SDprop be used - `session`: The session of a shiny process ## Returns The parameters of distribution of values below or above the detection limit. ## Details cutter returns the fitted distribution without cut ## Examples ```r ## Not run: library(HelpersMG) # _______________________________________________________________ # right censored distribution with gamma distribution # _______________________________________________________________ # Detection limit DL <- 100 # Generate 100 random data from a gamma distribution obc <- rgamma(100, scale=20, shape=2) # remove the data below the detection limit obc[obc>DL] <- +Inf # search for the parameters the best fit these censored data result <- cutter(observations=obc, upper_detection_limit=DL, cut_method="censored") result plot(result, xlim=c(0, 150), breaks=seq(from=0, to=150, by=10), col.mcmc=NULL) plot(result, xlim=c(0, 150), breaks=seq(from=0, to=150, by=10)) # _______________________________________________________________ # The same data seen as truncated data with gamma distribution # _______________________________________________________________ obc <- obc[is.finite(obc)] # search for the parameters the best fit these truncated data result <- cutter(observations=obc, upper_detection_limit=DL, cut_method="truncated") result plot(result, xlim=c(0, 150), breaks=seq(from=0, to=150, by=10)) # _______________________________________________________________ # left censored distribution with gamma distribution # _______________________________________________________________ # Detection limit DL <- 10 # Generate 100 random data from a gamma distribution obc <- rgamma(100, scale=20, shape=2) # remove the data below the detection limit obc[obcUDL] <- +Inf # search for the parameters the best fit these truncated data result1_gamma <- cutter(observations=obc, lower_detection_limit=LDL, upper_detection_limit = UDL, distribution="gamma", cut_method="censored", n.iter=5000, debug=0) result1_normal <- cutter(observations=obc, lower_detection_limit=LDL, upper_detection_limit = UDL, distribution="normal", cut_method="censored", n.iter=5000) result1_lognormal <- cutter(observations=obc, lower_detection_limit=LDL, upper_detection_limit = UDL, distribution="lognormal", cut_method="censored", n.iter=5000) result1_Weibull <- cutter(observations=obc, lower_detection_limit=LDL, upper_detection_limit = UDL, distribution="Weibull", cut_method="censored", n.iter=5000) result1_generalized.gamma <- cutter(observations=obc, lower_detection_limit=LDL, upper_detection_limit = UDL, distribution="generalized.gamma", cut_method="censored", n.iter=5000) result2_gamma <- cutter(observations=obc, lower_detection_limit=LDL, upper_detection_limit = UDL, distribution="gamma", n.mixture=2, cut_method="censored", n.iter=5000) result2_normal <- cutter(observations=obc, lower_detection_limit=LDL, upper_detection_limit = UDL, distribution="normal", n.mixture=2, cut_method="censored", n.iter=5000) result2_lognormal <- cutter(observations=obc, lower_detection_limit=LDL, upper_detection_limit = UDL, distribution="lognormal", n.mixture=2, cut_method="censored", n.iter=5000) result2_Weibull <- cutter(observations=obc, lower_detection_limit=LDL, upper_detection_limit = UDL, distribution="Weibull", n.mixture=2, cut_method="censored", n.iter=5000) result2_generalized.gamma <- cutter(observations=obc, lower_detection_limit=LDL, upper_detection_limit = UDL, distribution="generalized.gamma", n.mixture=2, cut_method="censored", n.iter=5000) compare_AIC(nomixture.gamma=result1_gamma, nomixture.normal=result1_normal, nomixture.lognormal=result1_lognormal, nomixture.Weibull=result1_Weibull, nomixture.generalized.gamma=result1_generalized.gamma, mixture.gamma=result2_gamma, mixture.normal=result2_normal, mixture.lognormal=result2_lognormal, mixture.Weibull=result2_Weibull, mixture.generalized.gamma=result2_generalized.gamma) plot(result2_gamma, xlim=c(0, 600), breaks=seq(from=0, to=600, by=10)) plot(result2_generalized.gamma, xlim=c(0, 600), breaks=seq(from=0, to=600, by=10)) # _______________________________________________________________ # left and right censored distribution # _______________________________________________________________ # Generate 100 random data from a gamma distribution obc <- rgamma(100, scale=20, shape=2) # Detection limit LDL <- 10 # remove the data below the detection limit obc[obcUDL] <- +Inf # search for the parameters the best fit these censored data result <- cutter(observations=obc, lower_detection_limit=LDL, upper_detection_limit=UDL, cut_method="censored") result plot(result, xlim=c(0, 150), col.DL=c("black", "grey"), col.unobserved=c("green", "blue"), breaks=seq(from=0, to=150, by=10)) # _______________________________________________________________ # Example with two values for lower detection limits # corresponding at two different methods of detection for example # with gamma distribution # _______________________________________________________________ obc <- rgamma(50, scale=20, shape=2) # Detection limit for sample 1 to 50 LDL1 <- 10 # remove the data below the detection limit obc[obc

cutter function