Java: random integer with non-uniform distribution -

how can create random integer n in java, between 1 , k "linear descending distribution", i.e. 1 likely, 2 less likely, 3 less likely, ..., k least likely, , probabilities descend linearly, this:

i know there dosens of threads on topic already, , apologize making new one, can't seem able create need them. know using import java.util.*;, code

random r=new random(); int n=r.nextint(k)+1; 

creates random integer between 1 , k, distributed uniformly.

generalization: hints creating arbitrarily distributed integer, i.e. f(n)=some function, p(n)=f(n)/(f(1)+...+f(k))), appreciated, example: .

this should give need:

public static int getlinnearrandomnumber(int maxsize){     //get linearly multiplied random number     int randommultiplier = maxsize * (maxsize + 1) / 2;     random r=new random();     int randomint = r.nextint(randommultiplier);      //linearly iterate through possible values find correct 1     int linearrandomnumber = 0;     for(int i=maxsize; randomint >= 0; i--){         randomint -= i;         linearrandomnumber++;     }      return linearrandomnumber; } 

also, here general solution positive functions (negative functions don't make sense) along range start index stopindex:

public static int getyourpositivefunctionrandomnumber(int startindex, int stopindex) {     //generate random number value ranges 0.0 sum of values of yourfunction possible integer return values startindex stopindex.     double randommultiplier = 0;     (int = startindex; <= stopindex; i++) {         randommultiplier += yourfunction(i);//yourfunction(startindex) + yourfunction(startindex + 1) + .. yourfunction(stopindex -1) + yourfunction(stopindex)     }     random r = new random();     double randomdouble = r.nextdouble() * randommultiplier;      //for each possible integer return value, subtract yourfunction value possible return value till below 0.  once below 0, return current value.       int yourfunctionrandomnumber = startindex;     randomdouble = randomdouble - yourfunction(yourfunctionrandomnumber);     while (randomdouble >= 0) {         yourfunctionrandomnumber++;         randomdouble = randomdouble - yourfunction(yourfunctionrandomnumber);     }      return yourfunctionrandomnumber; } 

note: functions may return negative values, 1 method take absolute value of function , apply above solution each yourfunction call.