# Quantile mapping using parametric transformations `fitQmapPTF` fits a parametric transformations to the quantile-quantile relation of observed and modelled values. `doQmapPTF` uses the transformation to adjust the distribution of the modelled data to match the distribution of the observations. ```r fitQmapPTF(obs, mod, ...) ## Default S3 method: fitQmapPTF(obs, mod, transfun=c("power","linear","expasympt", "scale","power.x0","expasympt.x0"), wet.day=TRUE, cost=c("RSS","MAE"), qstep=0.001,opar,...) ## S3 method for class 'matrix' fitQmapPTF(obs, mod, ...) ## S3 method for class 'data.frame' fitQmapPTF(obs, mod, ...) doQmapPTF(x,fobj,...) ## Default S3 method: doQmapPTF(x,fobj,...) ## S3 method for class 'matrix' doQmapPTF(x,fobj,...) ## S3 method for class 'data.frame' doQmapPTF(x,fobj,...) ``` ## Arguments - `obs`: `numeric` vector, column `matrix` or `data.frame` with observed time series. - `mod`: `numeric` vector, column `matrix` or `data.frame` with modelled time series, corresponding to `obs`. - `transfun`: either a character string specifying a predefined function used for the transformation (see Details) or a function with `x` as first argument e.g. `function(x,a,b){a*x^b}` - `wet.day`: `logical` indicating whether to perform wet day correction or not. OR a `numeric` threshold below which all values are set to zero. See Details. - `cost`: Criterion for optimisation. "RSS" minimises the residual sum of squares and produces a least square fit. "MAE" minimises the mean absolute error, which is less sensitive to outliers. - `qstep`: `NULL` or a numeric value between 0 and 1. See Details. - `opar`: a named list with arguments passed to `optim`. Note that `method` is chosen automatically. If `transfun` is a character string default values for `par` are available (but can be overwritten). See examples. - `x`: `numeric` vector or a column `matrix` of modelled time series - `fobj`: output from `fitQmapDIST` - ``...``: Further arguments passed to methods ## Details Before further computations the empirical cumulative distribution functions (CDF) of the observed (`obs`) and modelled (`mod`) are estimated. If `!is.null(qstep)` than `mod` and `obs` are aggregated to quantiles before model identification as: `quantile(x,probs=seq(0,1,by=qstep)`. If `!is.null(qstep)` than `mod` and `obs` are sorted to produce an estimate of the empirical CDF. In case of different length of `mod` and `obs` than `quantile(x,probs=seq(0,1,len=n)]` is used, where `n <- min(length(obs),length(mod))`. NOTE that large values of `qstep` effectively reduce the sample-size and can be used to speedup computations - but may render estimates less reliable. `wet.day` is intended for the use for precipitation data. Wet day correction attempts to equalise the fraction of days with precipitation between the observed and the modelled data. If `wet.day=TRUE` the empirical probability of nonzero observations is found (`obs>=0`) and the corresponding modelled value is selected as a threshold. All modelled values below this threshold are set to zero. If `wet.day` is `numeric` the same procedure is performed after setting all `obs

fitqmapptf function