lmomco (version 1.7.3)

z.par2cdf: Cumulative Distribution Function of Blipped Distributions

Description

This function acts as a front end of dispatcher to the distribution-specific cumulative distribution functions. $$x(F) = 0$$ for $0 \le F \le p$ and $$x_G\left(\frac{F-p}{1-p}\right)$$ for $F > p$.

Usage

z.par2cdf(x,p,para,z=0,...)

Arguments

x

A real value.

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 similar.

z

Threshold value.

...

The additional arguments are passed to the cumulative distribution function such as paracheck=FALSE for the Generalized Lambda distribution (cdfgld).

Value

• Nonexceedance probability ($0 \le F \le 1$) for x.

See Also

z.par2qua, par2cdf

Examples

# see the example for z.par2qua for more context
## 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,0,0,0,0)) # add of zero observations

# next compute the parameters for the positive data
gpa <- 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() # handy values, to get nice range of x
x <- z.par2qua(F,p,gpa) # x are now computed

PP <- pp(fake.data) # compute plotting positions of sim. sample

plot(PP,fake.data,ylim=c(0,5000)) # plot the sample
lines(cdfgpa(x,the.gpa),x) # the parent (without zeros)
lines(z.par2cdf(x,p,gpa),x,lwd=3) # fitted model with zero conditional

# now repeat the above code over and over again and watch the results