[Java] 数据分析--统计

二项分布

• 需求：5个四面体筛子，筛子三面绿色，一面红色，模拟1000000次，统计每次试验红色落地筛子个数的分布
• 实现：用循环实现5个筛子和1000000次试验，定义函数numRedDown模拟5个筛子试验结果，redDown模拟单次试验结果

Simulation.java

import java.util.Random;

public class Simulation{
    static final Random RANDOM = new Random();
    static final int n = 5;
    static final int N = 1000000;

    public static void main(String[] args){
        double[] dist = new double[n+1];
        for(int i = 0; i < N ; i++){
            int x = numRedDown(n);
            ++dist[x];
        }
        for(int i = 0; i <=n;i++){
            System.out.printf("%4d%8.4f%n",i,dist[i]/N);
        }
    }

    static boolean redDown(){
        int m = RANDOM.nextInt(4);
        return (m==0);
    }

    static int numRedDown(int n){
        int numRed = 0;
        for(int i = 0; i < n; i++){
            if(redDown()){
                ++numRed;
            }
        }
        return numRed;
    }
}

BinomialDistrabutionTester.java

import org.apache.commons.math3.distribution.BinomialDistribution;

public class BinomialDistributionTester {
    static final int n = 5;
    static final double p = 0.25;
    
    public static void main(String[] args) {
        BinomialDistribution bd = new BinomialDistribution(n, p);
        for (int x = 0; x <= n; x++) {
            System.out.printf("%4d%8.4f%n", x, bd.probability(x));
        }
        System.out.printf("mean = %6.4f%n", bd.getNumericalMean());
        double variance = bd.getNumericalVariance();
        double stdv = Math.sqrt(variance);
        System.out.printf("standard deviation = %6.4f%n", stdv);
    }
}

0 0.2381
1 0.3954
2 0.2629
3 0.0880
4 0.0145
5 0.0010

协方差

• 需求：生成1000个随机数对(x,y)，并计算x和y的相关系数
• 实现：Apache Commons Math library 中相应方法

import java.util.Random;
import org.apache.commons.math3.stat.correlation.Covariance;
import org.apache.commons.math3.stat.descriptive.moment.Variance;

public class CorrelationExample {
    static final Random RANDOM = new Random();
    static double[][] data1 = random(1000);
    static double[][] data2 = {{1, 2, 3, 4, 5}, {1, 3, 5, 7, 9}};
    static double[][] data3 = {{1, 2, 3, 4, 5}, {9, 8, 7, 6, 5}};

    public static void main(String[] args) {
        System.out.printf("rho1 = %6.3f%n", rho(data1));
        System.out.printf("rho2 = %6.3f%n", rho(data2));
        System.out.printf("rho3 = %6.3f%n", rho(data3));
    }
    
    static double[][] random(int n) {
        double[][] a = new double[2][n];
        for (int i = 0; i < n; i++) {
            a[0][i] = RANDOM.nextDouble();
            a[1][i] = RANDOM.nextDouble();
        }
        return a;
    }
    
    static double rho(double[][] data) {
        Variance v = new Variance();
        double varX = v.evaluate(data[0]);
        double sigX = Math.sqrt(varX);
        double varY = v.evaluate(data[1]);
        double sigY = Math.sqrt(varY);
        Covariance c = new Covariance(data);
        double sigXY = c.covariance(data[0], data[1]);
        return sigXY/(sigX*sigY);
    }
}

rho1 = -0.036
rho2 = 1.000
rho3 = -1.000

正态分布

• 需求：模拟均值16，标准差2.82的正态分布
• 实现：Apache Commons Math library 的 NomorDistribution类

import org.apache.commons.math3.distribution.NormalDistribution;

public class NormalDistributionTester {
    static int n = 32;
    static double p = 0.5;
    static double mu = n*p;
    static double sigma = Math.sqrt(n*p*(1-p));

    public static void main(String[] args) {
        NormalDistribution nd = new NormalDistribution(mu, sigma);
        
        double a = 17.5, b = 21.5;
        double Fa = nd.cumulativeProbability(a);
        System.out.printf("F(a) = %6.4f%n", Fa);
        double Fb = nd.cumulativeProbability(b);
        System.out.printf("F(b) = %6.4f%n", Fb);
        System.out.printf("F(b) - F(a) = %6.4f%n", Fb - Fa);
    }
}

F(a) = 0.7021
F(b) = 0.9741
F(b) - F(a) = 0.2720