Java：具有非均匀分布的随机整数 [英] Java: random integer with non-uniform distribution

问题描述

如何在Java中创建一个随机整数 n ，在 1 和 k之间带有线性递减分布，即 1 最有可能， 2 少于可能， 3 不太可能，......， k 最不可能，并且概率线性下降，如下所示：

How can I create a random integer n in Java, between 1 and k with a "linear descending distribution", i.e. 1 is most likely, 2 is less likely, 3 less likely, ..., k least likely, and the probabilities descend linearly, like this:

我知道已经有关于这个主题的线程问题，我为制作新主题而道歉，但我似乎无法从他们那里创造我需要的东西。我知道使用 import java.util。*; ，代码

I know that there are dosens of threads on this topic already, and I apologize for making a new one, but I can't seem to be able to create what I need from them. I know that using import java.util.*;, the code

Random r=new Random();
int n=r.nextInt(k)+1;

在 1 和<之间创建一个随机整数code> k ，统一分配。

GENERALIZATION：创建任意分布整数的任何提示，即 f（n）=某个函数， P（n）= f（n）/（f（1）+ ... + f（k））），也将不胜感激，例如：
。

GENERALIZATION: Any hints for creating an arbitrarily distributed integer, i.e. f(n)=some function, P(n)=f(n)/(f(1)+...+f(k))), would also be appreciated, for example: .

推荐答案

这应该可以满足您的需求：

This should give you what you need:

public static int getLinnearRandomNumber(int maxSize){
    //Get a linearly multiplied random number
    int randomMultiplier = maxSize * (maxSize + 1) / 2;
    Random r=new Random();
    int randomInt = r.nextInt(randomMultiplier);

    //Linearly iterate through the possible values to find the correct one
    int linearRandomNumber = 0;
    for(int i=maxSize; randomInt >= 0; i--){
        randomInt -= i;
        linearRandomNumber++;
    }

    return linearRandomNumber;
}

此外，这里是POSITIVE函数的一般解决方案（否定函数不确实有意义）从start index到stopIndex的范围：

Also, here is a general solution for POSITIVE functions (negative functions don't really make sense) along the range from start index to stopIndex:

public static int getYourPositiveFunctionRandomNumber(int startIndex, int stopIndex) {
    //Generate a random number whose value ranges from 0.0 to the sum of the values of yourFunction for all the possible integer return values from startIndex to stopIndex.
    double randomMultiplier = 0;
    for (int i = startIndex; i <= 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 for that possible return value till you get below 0.  Once you get below 0, return the current value.  
    int yourFunctionRandomNumber = startIndex;
    randomDouble = randomDouble - yourFunction(yourFunctionRandomNumber);
    while (randomDouble >= 0) {
        yourFunctionRandomNumber++;
        randomDouble = randomDouble - yourFunction(yourFunctionRandomNumber);
    }

    return yourFunctionRandomNumber;
}

注意：对于可能返回负值的函数，可以采用一种方法该函数的绝对值，并将其应用于每个yourFunction调用的上述解决方案。

Note: For functions that may return negative values, one method could be to take the absolute value of that function and apply it to the above solution for each yourFunction call.

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