R Plot Steep Slope Curve

Question

I want to draw a curve which has very steep gradients at the Cartesian coordinates x=0 and x=1 .

I tried to generate weighted plot points according to its slope. But I did not succeed.

---

Code for above plot

# Plot points weighted for gradient (My attempt)
ll <- stats::rchisq(100, 1)
lll <- 0.99 + ll
l <- append(ll, lll)

# Definition of curve
x <- 1 - exp(-l)
y <- 1 - stats::pnorm(0.3*stats::qnorm( exp(-l) ) - 0.5)

# Curve through precisely at (x, y) = (0, 0) and (1, 1)
plot(x, y, xlim = c(0, 1), ylim = c(0, 1))

---

My desired plot

---

Edit

Using the answer of @TavoGLC, I could do almost perfect plot. In my package, the number 0.3 and 0.5 in the definition y <- 1 - stats::pnorm(0.3*stats::qnorm( exp(-l) ) - 0.5) changes so, in the following I use 0.13 and 0.19 instead of the 0.3 and 0.5 .

Answer 1

I think that changing the weigths to a logarithmic wiight you can get a better approximation of the intended graph. The domain range is divided in three regions, the extreme regions are weighted with logspace generated values and the middle section is weigthed with linspace generated values.

library(pracma)
l0<-logspace(-15, 0, 25)
l2<-linspace(0, 1.5, 25)
l3<-logspace(0,3, 25)

la<-append(l0,l2)
l<-append(la,l3)
# definition of curve
x<- 1-exp(-l)
y <- 1-stats::pnorm(0.3*stats::qnorm( exp(-l ) )-0.5)

plot(x,y,xlim=c(0,1),ylim=c(0,1))

You can change the lower and upper boundaries from logspace or linspace to get a better result. Hope it helps