# Blipping Cumulative Distribution Functions This function acts as a front end or dispatcher to the distribution-specific cumulative distribution functions but also provides for blipping according to [REMOVE_ME]$$ F(x) = 0 [REMOVE_ME_2]$$ for $x \le z$ and [REMOVE_ME]$$ F(x) = p + (1-p)G(x) [REMOVE_ME_2]$$ for $x > z$ where $z$ is a threshold value. 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 $x(F)$ (`z.par2qua`). Lastly, please refer to the finiteness check in the Examples to see how one might accommodate $-\infty$ for $F = 0$ on a standard normal variate plot. A recommended practice when working with this function is the insertion of the $x$ value at $F=p$. Analogous practice is suggested for `z.par2qua` (see that documentation). ## Description This function acts as a front end or dispatcher to the distribution-specific cumulative distribution functions but also provides for blipping according to $$ F(x) = 0 $$ for $x \le z$ and $$ F(x) = p + (1-p)G(x) $$ for $x > z$ where $z$ is a threshold value. 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 $x(F)$ (`z.par2qua`). Lastly, please refer to the finiteness check in the Examples to see how one might accommodate $-\infty$ for $F = 0$ on a standard normal variate plot. A recommended practice when working with this function is the insertion of the $x$ value at $F=p$. Analogous practice is suggested for `z.par2qua` (see that documentation). ```r z.par2cdf(x, p, para, z=0, ...) ``` ## Arguments - `x`: A real value vector. - `p`: Nonexceedance probability of the `z` value. This probability could simply be the portion of record having zero values if `z=0`. - `para`: The parameters from `lmom2par` or `vec2par`. - `z`: Threshold value. - `...`: The additional arguments are passed to the cumulative distribution function such as `paracheck=FALSE` for the Generalized Lambda distribution (`cdfgld`). ## Returns Nonexceedance probability ($0 \le F \le 1$) for `x`. ## 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.par2qua`, `par2cdf` ## Examples ```r set.seed(21) 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 # going to tick to the inside and title right axis as well, so change some # plotting parameters par(mgp=c(3,0.5,0), mar=c(5,4,4,3)) # 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) # The following x vector obviously contains zero, so no need to insert it. x <- seq(-100, max(fake.data)) # absurd for x<0, but testing implementation PP <- pp(fake.data) # compute plotting positions of sim. sample plot(fake.data, qnorm(PP), xlim=c(0,4000), yaxt="n", ylab="") # plot the sample add.lmomco.axis(las=2, tcl=0.5, side=2, twoside=FALSE, side.type="NPP", otherside.type="SNV") lines(quagpa(F,gpa.all), qF) # the parent (without zeros) cdf <- qnorm(z.par2cdf(x,p,gpa.nzo)) cdf[! is.finite(cdf)] <- min(fake.data,qnorm(PP)) # See above documentation lines(x, cdf,lwd=3) # fitted model with zero conditional # now repeat the above code over and over again and watch the results par(mgp=c(3,1,0), mar=c(5,4,4,2)+0.1) # restore defaults ```

z.par2cdf function