How to shift data in a distribution in Java

Question

I am designing a software in Java, one of its functionalities is calculating the cumulative distribution of certain value in the distribution.

For example: The average marriage age in a country 28 old (which is the mean in the distribution), the distribution that i am using is chi-square (class ChiSquaredDistribution) with degree of freedom(3), since it resembles age at marriage distribution in the real world.

My goal is: if the user type their age, the output would be an approximate percentage of them getting married at that age (one year boundary) based on that distribution. something like: input : 30 years >>> output : 5.1% , input : 28 years>>> output :6% , input : 56 years>>> output :0.8% . The input is int, output is double

the problem is, the distribution starts at (0), and the mean is i believe (3) by default, the following code i wrote displays marriage probability from the age 0 to 70, my question is how to shift it to 18 and over, with the mean of the average age at marriage ?

ChiSquaredDistribution x = new ChiSquaredDistribution(3); 
Random r = new Random();
for (int UserAtAge=0; UserAtAge<70; UserAtAge++) {
    System.out.println((x.cumulativeProbability(UserAtAge+1)-x.cumulativeProbability(UserAtAge))*100);  
}

Two images attached for current results, and the intended results. Any code and help would highly be appreciated.

See the current results and the desired results

Answer 1

Shift your distribution by subtracting 18 from each value, so 18 maps to 0, 28 maps to 10, 70 maps to 52, etc. The mean of an unshifted chi-square is its degrees of freedom. Using a chi-square(3) would yield a mean of 21 for the shifted data, so you'll want to bump that up to a chi-square(10) to yield a mean of 28 with the shift.

With some cleanup (lower-case start for local variables, r was unused), the shifted version is:

ChiSquaredDistribution x = new ChiSquaredDistribution(10); 
for (int userAge=18; userAge<71; userAge++) {
    System.out.println((x.cumulativeProbability(userAge + 1 - 18) - x.cumulativeProbability(userAge - 18)) * 100);  
}