java - Java 高斯分布-钟形曲线

Question

我已经计算了一组值的平均值和 SD。现在我需要使用这些值绘制钟形曲线来显示 JAVA Swing 中的正态分布。我该如何处理这种情况。

名单：204 297 348 528 681 684 785 957 1044 1140 1378 1545 1818

总数：13

平均值（平均值）：877.615384615385

标准偏差（SD）：477.272626245539

如果我可以得到 x 和 y 坐标，我可以做到，但我如何得到这些值？

Answer 1

First you need to calculate the variance for the set. The variance is computed as the average squared deviation of each number from its mean.

double variance(double[] population) {
        long n = 0;
        double mean = 0;
        double s = 0.0;

        for (double x : population) {
                n++;
                double delta = x – mean;
                mean += delta / n;
                s += delta * (x – mean);
        }
        // if you want to calculate std deviation

        return (s / n);
}

Once you have that you can choose x depending on your graph resolution compared to your value set spread and plug it in to the following equation to get y.

protected double stdDeviation, variance, mean; 

    public double getY(double x) { 

        return Math.pow(Math.exp(-(((x - mean) * (x - mean)) / ((2 * variance)))), 1 / (stdDeviation * Math.sqrt(2 * Math.PI))); 

    } 

To display the resulting set: say we take the population set you laid out and decide you want to show x=0 to x=2000 on a graph with an x resolution of 1000 pixels. Then you would plug in a loop (int x = 0; x <= 2000; x = 2) and feed those values into the equation above to get your y values for the pair. Since the y you want to show is 0-1 then you map these values to whatever you want your y resolution to be with appropriate rounding behavior so your graph doesn't end up too jaggy. So if you want your y resolution to be 500 pixels then you set 0 to 0 and 1 to 500 and .5 to 250 etc. etc. This is a contrived example and you might need a lot more flexibility but I think it illustrates the point. Most graphing libraries will handle these little things for you.

Answer 2

这是使用XChart绘制一些高斯曲线的示例。代码可以在这里找到。免责声明：我是 XChart Java 图表库的创建者。

public class ThemeChart03 implements ExampleChart {

  public static void main(String[] args) {

    ExampleChart exampleChart = new ThemeChart03();
    Chart chart = exampleChart.getChart();
    new SwingWrapper(chart).displayChart();
  }

  @Override
  public Chart getChart() {

    // Create Chart
    Chart_XY chart = new ChartBuilder_XY().width(800).height(600).theme(ChartTheme.Matlab).title("Matlab Theme").xAxisTitle("X").yAxisTitle("Y").build();

    // Customize Chart
    chart.getStyler().setPlotGridLinesVisible(false);
    chart.getStyler().setXAxisTickMarkSpacingHint(100);

    // Series
    List<Integer> xData = new ArrayList<Integer>();
    for (int i = 0; i < 640; i++) {
      xData.add(i);
    }
    List<Double> y1Data = getYAxis(xData, 320, 60);
    List<Double> y2Data = getYAxis(xData, 320, 100);
    List<Double> y3Data = new ArrayList<Double>(xData.size());
    for (int i = 0; i < 640; i++) {
      y3Data.add(y1Data.get(i) - y2Data.get(i));
    }

    chart.addSeries("Gaussian 1", xData, y1Data);
    chart.addSeries("Gaussian 2", xData, y2Data);
    chart.addSeries("Difference", xData, y3Data);

    return chart;
  }

  private List<Double> getYAxis(List<Integer> xData, double mean, double std) {

    List<Double> yData = new ArrayList<Double>(xData.size());

    for (int i = 0; i < xData.size(); i++) {
      yData.add((1 / (std * Math.sqrt(2 * Math.PI))) * Math.exp(-(((xData.get(i) - mean) * (xData.get(i) - mean)) / ((2 * std * std)))));
    }
    return yData;
  }

}

结果图如下所示：