# Blipping Quantile Functions This function acts as a front end or dispatcher to the distribution-specific quantile functions but also provides for blipping for zero (or other) threshold according to [REMOVE_ME]$$ x(F) = 0 [REMOVE_ME_2]$$ for $0 \le F \le p$ and [REMOVE_ME]$$ x_G\left(\frac{F-p}{1-p}\right) [REMOVE_ME_2]$$ for $F > p$. This function is generalized for $z \ne 0$. The $z$ is not tracked as part of the parameter object. This might arguably be a design flaw, but the function will do its best to test whether the $z$ given is compatable (but not necessarily equal to $\hat{x} = x(0)$) with the quantile function $x(F)$. A recommended practice when working with this function when $F$ values are generated for various purposes, such as for graphics, then the value of $p$ should be inserted into the vector, and the vector obviously sorted (see the line using the `nonexceeds` function). This should be considered as well when `z.par2cdf` is used but with the insertion of the $x$ value at $F=p$. ## Description This function acts as a front end or dispatcher to the distribution-specific quantile functions but also provides for blipping for zero (or other) threshold according to $$ x(F) = 0 $$ for $0 \le F \le p$ and $$ x_G\left(\frac{F-p}{1-p}\right) $$ for $F > p$. This function is generalized for $z \ne 0$. The $z$ is not tracked as part of the parameter object. This might arguably be a design flaw, but the function will do its best to test whether the $z$ given is compatable (but not necessarily equal to $\hat{x} = x(0)$) with the quantile function $x(F)$. A recommended practice when working with this function when $F$ values are generated for various purposes, such as for graphics, then the value of $p$ should be inserted into the vector, and the vector obviously sorted (see the line using the `nonexceeds` function). This should be considered as well when `z.par2cdf` is used but with the insertion of the $x$ value at $F=p$. ```r z.par2qua(f, p, para, z=0, ...) ``` ## Arguments - `f`: Nonexceedance probabilities ($0 \le F \le 1$). - `p`: Nonexceedance probability of `z` value. - `para`: The parameters from `lmom2par` or `vec2par`. - `z`: Threshold value. - `...`: The additional arguments are passed to the quantile function such as `paracheck = FALSE` for the Generalized Lambda distribution (`quagld`). ## Returns Quantile value for $f$. ## Author(s) W.H. Asquith ## References Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: Createspace Independent Publishing Platform, ISBN 978--146350841--8. ## See Also `z.par2cdf`, `par2qua` ## Examples ```r # define the real parent (or close) the.gpa <- vec2par(c(100,1000,0.1),type='gpa') fake.data <- rlmomco(30,the.gpa) # simulate some data fake.data <- sort(c(fake.data, rep(0,10))) # add some zero observations par(mgp=c(3,0.5,0)) # going to tick to the inside, change some parameters # next compute the parameters for the positive data gpa.all <- pargpa(lmoms(fake.data)) gpa.nzo <- pargpa(lmoms(fake.data[fake.data > 0])) n <- length(fake.data) # sample size p <- length(fake.data[fake.data == 0])/n # est. prob of zero value F <- nonexceeds(sig6=TRUE); F <- sort(c(F,p)); qF <- qnorm(F) PP <- pp(fake.data) # compute plotting positions of sim. sample plot(qnorm(PP), fake.data, ylim=c(0,4000), xaxt="n", xlab="") # plot the sample add.lmomco.axis(las=2, tcl=0.5, twoside=TRUE, side.type="SNV", otherside.type="NA") lines(qF,quagpa(F,gpa.all)) # the parent (without zeros) lines(qF,z.par2qua(F,p,gpa.nzo),lwd=3) # fitted model with zero conditional par(mgp=c(3,1,0)) # restore defaults ```

z.par2qua function