Why is 'curve' so different from 'lines' and 'points' in R?

Question

I would like to fit the frequency data with discrete generalized beta distribution (DGBD).

The data look like this:

freq = c(1116, 2067, 137 ,  124, 643,  2042, 55  ,47186,  7504, 1488, 211,   1608,   
         3517 , 7  , 896  ,  378, 17 ,3098, 164977  ,  601 ,  196, 637, 149 , 44,2 ,  1801, 882   , 636,5184,  1851,  776 ,   343   , 851, 33  ,4011,   209,  715 , 
         937 , 20,   6922, 2028 , 23,  3045 , 16 , 334,  31 ,  2)

Rank = rank(-freq, ties.method = c("first") )
p = freq/sum(freq)

get the log forms

log.f = log(freq)
log.p = log(p)
log.rank = log(Rank)
log.inverse.rank = log(length(Rank)+1-Rank)

linear regression of the discrete generalized beta distribution

co=coef(lm(log.p~log.inverse.rank + log.rank))
zmf = function(x) exp(co[[1]]+ co[[2]]*log(length(x)+1-x) + co[[3]]*log(x))

plot

plot(p~Rank, xlim = c(1, 80), log = "xy",xlab = "Rank (log)", ylab = "Probability (log)")
curve(zmf, col="blue", add = T)
xx=c(1:length(Rank))
lines(zmf(xx)~xx, col = "red")
points(zmf(xx)~xx, col = "purple")

Figure 1. the plot looks like this

My question is what is the right way to demonstrate the result? lines (points) or curve?

Update:

Although I have not figured out the underling logic, the solution is found:

@Frank reminds me to notice the trick of setting the length of n in the curve. It solves the problem. Thus, n in curve is necessary when we try to fit the raw data. Although in many situations, n is ignored.

plot(p~Rank, log = "xy",xlab = "Rank (log)", ylab = "Probability (log)")
curve(zmf, col="blue", add = T, n = length(Rank)) # set the the number of x values at which to evaluate.

　Figure 2 The right way to use curve: specify the 'n'

Answer 1

The reason you need to specify the n here is because your function depends on length(x)!

zmf = function(x) exp(co[[1]]+ co[[2]]*log(length(x)+1-x) + co[[3]]*log(x))
                                           ^^^^^^^^^

Here the length of the x's provided to your function by curve is n!

Here is your plot if you stick with the default n=101 but feed your line and points with a vector xx of length 101:

plot(p~Rank, xlim = c(1,80), log = "xy",xlab = "Rank (log)", ylab = "Probability (log)")
curve(zmf, col="blue", add = T)
xx=seq(1,length(Rank),length.out=101)
lines(zmf(xx)~xx, col = "red")
points(zmf(xx)~xx, col = "purple")

Neither voodoo nor bug ! :)