How to get a random Date with linear distribution?

I'd like to have a random millisecond value from an (inverse) linear distribution of values (if I get the term right).

In essence I want to have a random point-in-time t (Date in my case) between two time points early and late where a t towards early has a much greater probability then those towards late. late itself may have a probability of 0.0.

My current java code just uses uniform distribution, so I plan to modify this to a (inverse) linear distribution:

public Date getRandomDate(Date early, Date late) {
  long diff = late.getTime() - early.getTime();
  final int randVal = rand.nextInt((int) diff);
  Calendar cal = Calendar.getInstance();
  cal.setTime(early);
  cal.add(Calendar.MILLISECOND, randVal);
  return cal.getTime();
}