import com.imsl.chart.*;
import com.imsl.chart.qc.*;
import com.imsl.stat.Cdf;
import com.imsl.stat.Sort;
import com.imsl.stat.LinearRegression;

public class SampleCumulativeProbability extends JFrameChart {    
    static final double timeBetweenFailures[] = {
        286, 948, 536, 124, 816, 729, 4, 143, 431, 8, 2837,
        596, 81, 227, 603, 492, 1199, 1214, 2831, 96
    };
    
    static final double ticks[] = {0.001, 0.005, 0.01, 0.02, 0.05,
        0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90,
        0.95, 0.98, 0.99, 0.995, 0.999
    };
    
    public SampleCumulativeProbability() {
        Chart chart = getChart();
        AxisXY axis = new AxisXY(chart);
        double a = ticks[0];
        double b = ticks[ticks.length-1];
        chart.getChartTitle().setTitle("Normal Probability Plot");
        Axis1D axisX = axis.getAxisX();
        axisX.getAxisTitle().setTitle("Transformed Time between failures");
        Axis1D axisY = axis.getAxisX();
        axisY.getAxisTitle().setTitle("Cummulative Probability");
        axisY.setTransform(axis.TRANSFORM_CUSTOM);
        Transform transform = new NormalTransform();
        axis.getAxisY().setCustomTransform(transform);
        axis.getAxisY().setAutoscaleInput(axis.AUTOSCALE_OFF);
        axis.getAxisY().setWindow(a, b);
        axis.getAxisY().setTextFormat("0.0%");
        axis.getAxisY().setTicks(ticks);
        axis.getAxisY().getMinorTick().setPaint(false);

        int n = timeBetweenFailures.length;
        double x[] = new double[n];
        double y[] = new double[n];
        for (int i = 0;  i < x.length;  i++) {
            x[i] = Math.pow(timeBetweenFailures[i], 1.0/3.6);
        }
        Sort.ascending(x);
        for (int i = 0;  i < x.length;  i++) {
            y[i] = (double)(i+0.5) / (double)n;
        }
        Data data = new Data(axis, x, y);
        data.setDataType(Data.DATA_TYPE_MARKER);
        data.setMarkerType(Data.MARKER_TYPE_FILLED_CIRCLE);
        
        /*
         * Compute an plot a regresssion line
         */
        LinearRegression lr = new LinearRegression(1, true);
        for (int i = 0;  i < n;  i++) {
            lr.update(new double[]{x[i]}, Cdf.inverseNormal(y[i]));
        }
        double coef[] = lr.getCoefficients();
        double lry[] = new double[x.length];
        for (int i = 0;  i < x.length;  i++) {
            lry[i] = Cdf.normal(coef[0]+coef[1]*x[i]);
        }
        Data lrData = new Data(axis, x, lry);
        lrData.setDataType(Data.DATA_TYPE_LINE);
        lrData.setLineColor("blue");
    }
    
    
    static class NormalTransform implements Transform {
        private double scaleA, scaleB;
        
        /**
         * Initializes the mappings between user and coordinate space.
         */
        public void setupMapping(Axis1D axis1d) {
            double w[] = axis1d.getWindow();
            double t = Cdf.inverseNormal(w[0]);
            scaleB = 1.0/(Cdf.inverseNormal(w[1])-t);
            scaleA = -scaleB*t;
        }
        
        /**
         * Maps a point in [0,1] to a probability.
         */
        public double mapUnitToUser(double unit) {
            return Cdf.normal((unit-scaleA)/scaleB);
        }
        
        /**
         * Maps a probablity to the interval [0,1].
         */
        public double mapUserToUnit(double p) {
            return scaleA + scaleB*Cdf.inverseNormal(p);
        }
    }
    
    public static void main(String argv[]) {
        new SampleCumulativeProbability().setVisible(true);
    }
}