有沒有辦法生成大范圍的亂數，但傾向于接近1的值？（爪哇）-有解無憂

我正在制作一個神經網路，我有一個weight乘以某個值的變數。我希望能夠隨機化weight變數并允許它是像 0.1 這樣的小數或像高達 10 這樣的大數。但是，我希望它通常更接近 1。

這是我希望隨機值看起來像的示例：

0.9, 0.6, 1.5, 0.2, 5.8, 1.1, 1.3, 0.8,2.6等

允許使用諸如 5.8 之類的值，但大多數值接近 1。

請讓我知道這是否可以在 Java 中完成。

非常感謝你！

uj5u.com熱心網友回復：

聽起來你想要一個泊松分布。通常，值的分布是離散的，由整數給出，例如 0、1、2 等，但您可以將結果除以 10 得到一位小數。

泊松隨機變數x的概率函式由以下公式給出：

f( x ) =(e ^–λ λ ^x )/ x !

Java 沒有內置任何東西來獲取泊松分布的隨機變數，但我們可以使用Random.nextDouble().

訣竅是將均勻隨機變數映射到泊松隨機變數。

Math.se 上的這個問答展示了如何使用數學將統一隨機變數映射到泊松隨機變數，方法是找到滿足條件的最小泊松隨機變數p，其中U是統一隨機變數，條件是U小于大于或等于作為p函式的累積概率分布。

p

P ≡ min { p = 0, 1, 2, ... | U ≤ exp(-λ) Σ (λ ^p )/ p ! }

我=0

這是我使用此方程撰寫的一些代碼，用于將統一隨機變數轉換urv為泊松隨機變數p。

public class Test {
    public static void main(String[] args) {
        double lambda = 10.0;
        System.out.println("Test");
        for (int urv100 = 0; urv100 < 100; urv100  ) {
            double urv = urv100 / 100.0;
            System.out.println("P("   lambda   ", "   urv   ") = "   poisson(lambda, urv));
        }
        System.out.println("Converting uniform to Poisson");
        Random rnd = new Random();
        for (int r = 0; r < 100; r  ) {
            double urv = rnd.nextDouble();
            System.out.println("urv of "   urv   " mapped to p of "   poisson(lambda, urv) / 10.0);
        }
        System.out.println("urv of 0.999999 mapped to p of "   poisson(lambda, 0.999999) / 10.0);
        System.out.println("urv of 0.999999999999 mapped to p of "   poisson(lambda, 0.999999999999) / 10.0);
        //System.out.println("urv of 0.9999999999999999 mapped to p of "   poisson(lambda, 0.9999999999999999) / 10.0);
    }
    public static int poisson(double lambda, double urv){
        int p = 0;
        while (true) {
            double cumulDistr = cumulDistr(lambda, p);
            //System.out.println("   cumulDistr("   lambda   ", "   p   ") is "   cumulDistr);
            if (urv <= cumulDistr) {
                return p;
            }
            p  ;
        }
    }

    private static double cumulDistr(double lambda, int p) {
        double summation = 0;
        for (int i = 0; i <= p; i  ) {
            summation  = Math.pow(lambda, i) / fact(i);
        }
        return summation * Math.exp(-lambda);
    }

    private static double fact(int p) {
        double product = 1;
        for (int f = 1; f <= p; f  ) {
            product *= f;
        }
        return product;
    }
}

該fact方法計算階乘，該cumulDistr方法計算累積泊松分布，該方法計算小于或等于累積分布poisson的最小值。變數是泊松分布的平均值。purvlambda

如果您想要一個 1.0 的平均值，但以 0.1 為增量的離散值，則將lambda 10您的結果除以10.

這是我的輸出。請注意，雖然5.8可能，但它可能非常罕見。

Test
P(10.0, 0.0) = 0
P(10.0, 0.01) = 3
P(10.0, 0.02) = 4
P(10.0, 0.03) = 5
P(10.0, 0.04) = 5
P(10.0, 0.05) = 5
P(10.0, 0.06) = 5
P(10.0, 0.07) = 6
P(10.0, 0.08) = 6
P(10.0, 0.09) = 6
P(10.0, 0.1) = 6
P(10.0, 0.11) = 6
P(10.0, 0.12) = 6
P(10.0, 0.13) = 6
P(10.0, 0.14) = 7
P(10.0, 0.15) = 7
P(10.0, 0.16) = 7
P(10.0, 0.17) = 7
P(10.0, 0.18) = 7
P(10.0, 0.19) = 7
P(10.0, 0.2) = 7
P(10.0, 0.21) = 7
P(10.0, 0.22) = 7
P(10.0, 0.23) = 8
P(10.0, 0.24) = 8
P(10.0, 0.25) = 8
P(10.0, 0.26) = 8
P(10.0, 0.27) = 8
P(10.0, 0.28) = 8
P(10.0, 0.29) = 8
P(10.0, 0.3) = 8
P(10.0, 0.31) = 8
P(10.0, 0.32) = 8
P(10.0, 0.33) = 8
P(10.0, 0.34) = 9
P(10.0, 0.35) = 9
P(10.0, 0.36) = 9
P(10.0, 0.37) = 9
P(10.0, 0.38) = 9
P(10.0, 0.39) = 9
P(10.0, 0.4) = 9
P(10.0, 0.41) = 9
P(10.0, 0.42) = 9
P(10.0, 0.43) = 9
P(10.0, 0.44) = 9
P(10.0, 0.45) = 9
P(10.0, 0.46) = 10
P(10.0, 0.47) = 10
P(10.0, 0.48) = 10
P(10.0, 0.49) = 10
P(10.0, 0.5) = 10
P(10.0, 0.51) = 10
P(10.0, 0.52) = 10
P(10.0, 0.53) = 10
P(10.0, 0.54) = 10
P(10.0, 0.55) = 10
P(10.0, 0.56) = 10
P(10.0, 0.57) = 10
P(10.0, 0.58) = 10
P(10.0, 0.59) = 11
P(10.0, 0.6) = 11
P(10.0, 0.61) = 11
P(10.0, 0.62) = 11
P(10.0, 0.63) = 11
P(10.0, 0.64) = 11
P(10.0, 0.65) = 11
P(10.0, 0.66) = 11
P(10.0, 0.67) = 11
P(10.0, 0.68) = 11
P(10.0, 0.69) = 11
P(10.0, 0.7) = 12
P(10.0, 0.71) = 12
P(10.0, 0.72) = 12
P(10.0, 0.73) = 12
P(10.0, 0.74) = 12
P(10.0, 0.75) = 12
P(10.0, 0.76) = 12
P(10.0, 0.77) = 12
P(10.0, 0.78) = 12
P(10.0, 0.79) = 12
P(10.0, 0.8) = 13
P(10.0, 0.81) = 13
P(10.0, 0.82) = 13
P(10.0, 0.83) = 13
P(10.0, 0.84) = 13
P(10.0, 0.85) = 13
P(10.0, 0.86) = 13
P(10.0, 0.87) = 14
P(10.0, 0.88) = 14
P(10.0, 0.89) = 14
P(10.0, 0.9) = 14
P(10.0, 0.91) = 14
P(10.0, 0.92) = 15
P(10.0, 0.93) = 15
P(10.0, 0.94) = 15
P(10.0, 0.95) = 15
P(10.0, 0.96) = 16
P(10.0, 0.97) = 16
P(10.0, 0.98) = 17
P(10.0, 0.99) = 18

Converting uniform to Poisson
urv of 0.8288520112341562 mapped to p of 1.3
urv of 0.35446366155650744 mapped to p of 0.9
urv of 0.8340486798727402 mapped to p of 1.3
urv of 0.8858928268763592 mapped to p of 1.4
urv of 0.9026643406946203 mapped to p of 1.4
urv of 0.13960555377413952 mapped to p of 0.7
urv of 0.9195710056013893 mapped to p of 1.5
urv of 0.44998928169297736 mapped to p of 0.9
urv of 0.8793009483663888 mapped to p of 1.4
urv of 0.8591855177365383 mapped to p of 1.3
urv of 0.5205437915100812 mapped to p of 1.0
urv of 0.8703983622023188 mapped to p of 1.4
urv of 0.82075096895357 mapped to p of 1.3
urv of 0.9806363370196562 mapped to p of 1.7
urv of 0.02509517057275079 mapped to p of 0.4
urv of 0.36375516077339465 mapped to p of 0.9
urv of 0.07037727036002717 mapped to p of 0.6
urv of 0.6818190760646871 mapped to p of 1.1
urv of 0.32197145361627577 mapped to p of 0.8
urv of 0.23745234391089698 mapped to p of 0.8
urv of 0.8934052227696372 mapped to p of 1.4
urv of 0.44142256004343283 mapped to p of 0.9
urv of 0.4021584936656427 mapped to p of 0.9
urv of 0.8982224754947559 mapped to p of 1.4
urv of 0.5358391491707077 mapped to p of 1.0
urv of 0.7385630250167211 mapped to p of 1.2
urv of 0.979775968296643 mapped to p of 1.7
urv of 0.22274327853351406 mapped to p of 0.8
urv of 0.07561592409103857 mapped to p of 0.6
urv of 0.06473994682056239 mapped to p of 0.5
urv of 0.5416987364902209 mapped to p of 1.0
urv of 0.4860980118260786 mapped to p of 1.0
urv of 0.9564072685131361 mapped to p of 1.6
urv of 0.19446735227769363 mapped to p of 0.7
urv of 0.7675862499420885 mapped to p of 1.2
urv of 0.4277105215574004 mapped to p of 0.9
urv of 0.8923336944675764 mapped to p of 1.4
urv of 0.9353143574875429 mapped to p of 1.5
urv of 0.5754775563481273 mapped to p of 1.0
urv of 0.449414823264646 mapped to p of 0.9
urv of 0.9109544383075693 mapped to p of 1.4
urv of 0.3837527451770203 mapped to p of 0.9
urv of 0.14283575366272117 mapped to p of 0.7
urv of 0.3866077468484732 mapped to p of 0.9
urv of 0.662249698097005 mapped to p of 1.1
urv of 0.05012298208977162 mapped to p of 0.5
urv of 0.12890274868435359 mapped to p of 0.6
urv of 0.7709717413863731 mapped to p of 1.2
urv of 0.7629124932757383 mapped to p of 1.2
urv of 0.08419512530357443 mapped to p of 0.6
urv of 0.9814512014328213 mapped to p of 1.7
urv of 0.01204516066988126 mapped to p of 0.4
urv of 0.8681197289737762 mapped to p of 1.4
urv of 0.2322137137936654 mapped to p of 0.8
urv of 0.6494975804996993 mapped to p of 1.1
urv of 0.4649550027050112 mapped to p of 1.0
urv of 0.36705272690857005 mapped to p of 0.9
urv of 0.08698141252662916 mapped to p of 0.6
urv of 0.24326648103541826 mapped to p of 0.8
urv of 0.9229172381814946 mapped to p of 1.5
urv of 0.08379005168736153 mapped to p of 0.6
urv of 0.6544487613989808 mapped to p of 1.1
urv of 0.18367321169511808 mapped to p of 0.7
urv of 0.6756484363119853 mapped to p of 1.1
urv of 0.13179611575336148 mapped to p of 0.7
urv of 0.2534425428679633 mapped to p of 0.8
urv of 0.16581779859681034 mapped to p of 0.7
urv of 0.9086216315426554 mapped to p of 1.4
urv of 0.11808111111941566 mapped to p of 0.6
urv of 0.28957878822961225 mapped to p of 0.8
urv of 0.8244607265851857 mapped to p of 1.3
urv of 0.8831380495463445 mapped to p of 1.4
urv of 0.2222095479898628 mapped to p of 0.8
urv of 0.5000703942445024 mapped to p of 1.0
urv of 0.3341765268545145 mapped to p of 0.9
urv of 0.033476169064498684 mapped to p of 0.5
urv of 0.2856853641247886 mapped to p of 0.8
urv of 0.8530540470203735 mapped to p of 1.3
urv of 0.3028587949037277 mapped to p of 0.8
urv of 0.8449176275299684 mapped to p of 1.3
urv of 0.9388444379027909 mapped to p of 1.5
urv of 0.403224473163457 mapped to p of 0.9
urv of 0.22447582249839637 mapped to p of 0.8
urv of 0.13523963178706166 mapped to p of 0.7
urv of 0.9652355645124876 mapped to p of 1.6
urv of 0.05497837319494847 mapped to p of 0.5
urv of 0.44545341748361267 mapped to p of 0.9
urv of 0.15230147439015596 mapped to p of 0.7
urv of 0.5575736794499111 mapped to p of 1.0
urv of 0.3649349046306235 mapped to p of 0.9
urv of 0.06878741747556394 mapped to p of 0.6
urv of 0.7216428916513631 mapped to p of 1.2
urv of 0.8546996873563696 mapped to p of 1.3
urv of 0.22761255830658056 mapped to p of 0.8
urv of 0.47096564927387896 mapped to p of 1.0
urv of 0.5305503681123561 mapped to p of 1.0
urv of 0.1655836111058504 mapped to p of 0.7
urv of 0.5312078242229661 mapped to p of 1.0
urv of 0.1390046501481954 mapped to p of 0.7
urv of 0.5188365074236052 mapped to p of 1.0
urv of 0.999999 mapped to p of 2.8
urv of 0.999999999999 mapped to p of 3.9

請注意，在嘗試獲得 a5.8時，我嘗試了 0.9999999999999999（16 個9十進制數字）。在我殺死它之前它運行了超過一分鐘。對于累積分布值，它一定已經達到了 a 的精度double，因此您必須針對這種極端情況添加某種防護措施。

您可能還希望將結果設定lambda為5.05 并將其除以以為增量的值0.2，這可能會將概率曲線加寬到足以（偶爾）得到 a 5.8。

uj5u.com熱心網友回復：

為此，您可以為隨機發生器提供比高值更多的低值。設定一個陣列來保存你的體重值，低值比高值多。然后隨機生成器創建一個索引。由于您有更多的低值，因此選擇低值的機會大于高值：

float[] values = new float[5];
values[0] = 0.1f;
values[1] = 0.1f;
values[2] = 0.2f;
values[3] = 0.2f;
values[4] = 10.0f;

隨機器回傳從 0 到 4 的索引。value的0.1和0.2被選擇的可能性是的兩倍10.0

您可以通過添加比高值更多的低值來調整權重。

uj5u.com熱心網友回復：

您可以從函式10 - log(x) for x from 1 to e^10中獲取一個值。

這將為您提供從 0 到 10 的值，這些值更可能是低而不是高。

Random r = new Random();
double max = Math.exp(10);

public double expWeight() {
    return 10 - Math.log(r.nextDouble(1, max));
}

double weight = expWeight();

但是，這也會使小于 1 的數字比 1 更有可能，這可能不是您想要的。

轉載請註明出處，本文鏈接：https://www.uj5u.com/gongcheng/474844.html

標籤：爪哇数学随机的

上一篇：在Markdown中創建標簽

下一篇：如何在C 中進行數值積分的基本示例