import java.awt.*;
import java.applet.Applet;
import java.util.Random;
import java.lang.Double;

/**
  Applet to demonstrate that sampling distributions converge to the
  population.  Uses a histogram plot of the sample and overlays it with
  the expected probability density function (PDF).  Also shows the
  expected and sample means.

  @Author: Suresh Srinivasan (suresh@thomtech.com)
  @Date: Oct 1995
  @Version: 0.1
  */
public class SamplingApplet extends java.applet.Applet {
    static final java.awt.Color BACKGROUNDCOLOR = Color.lightGray;

    String distributionNames[] = {
	"Gaussian", "Exponential", "Uniform"
    };
    Label statusLabel;
    ControlPanel controlPanel;
    GraphPanel graphPanel;
    StatusPanel statusPanel;
    DataPanel dataPanel;
    Distribution distribution;
    
    public void init() {
	setLayout(new BorderLayout());

/* Panel to attach the control and data panels */
	Panel p = new Panel();
	p.setLayout(new GridLayout(1, 2));
	controlPanel = new ControlPanel(this);
	dataPanel = new DataPanel(this);
	p.add(controlPanel);
	p.add(dataPanel);
	add("North", p);

	graphPanel = new GraphPanel(this);
	add("Center", graphPanel);

	statusPanel = new StatusPanel(this);
	add("South", statusPanel);

/* this should cause each component in this layout to compute their sizes */
	layout();

/* start the thread for the graph */
	graphPanel.start();
    }

    public static void main(String args[]) {
	Frame f = new Frame("Sampling Distributions");
	SamplingApplet applet = new SamplingApplet();

	applet.init();

	f.add("Center", applet);
	f.resize(500, 400);
	f.pack();
	f.show();

	applet.start();
    }
}

class ControlPanel extends Panel {
    public final static String STARTSTRING = "Start";
    public final static String STOPSTRING = "Stop";
    public final static String PAUSESTRING = "Pause";
    public final static String RESUMESTRING = "Resume";

    public final static Font BUTTONFONT = new Font("Dialog", Font.BOLD, 12);
    public final static Font CHOICEFONT = new Font("Dialog", Font.PLAIN, 12);
    public final static Font ERRORFONT = new Font("TimesRoman", Font.BOLD, 20);

    SamplingApplet applet;
    Button startButton;
    Button pauseButton = new Button(PAUSESTRING);
    Choice distributionChoice;
    
    public ControlPanel(SamplingApplet applet) {
	this.applet = applet;
	setLayout(new FlowLayout(FlowLayout.LEFT, 10, 10));

	startButton = new Button();
	startButton.setFont(BUTTONFONT);
	startButton.setLabel(STARTSTRING);
	add(startButton);

	pauseButton = new Button();
	pauseButton.setFont(BUTTONFONT);
	pauseButton.setLabel(PAUSESTRING);
	add(pauseButton);

	distributionChoice = new Choice();
	distributionChoice.setFont(CHOICEFONT);

	for (int i=0; i<applet.distributionNames.length; i++)
	    distributionChoice.addItem(applet.distributionNames[i]);
	add(distributionChoice);

	reset(StatusPanel.NULLSTRING);
    }

    public boolean action(Event e, Object o) {
	if (e.target instanceof Choice) {

	    applet.graphPanel.current = ((Choice)(e.target)).getSelectedIndex();
	    applet.graphPanel.initialize();
	    applet.graphPanel.makeNotReady();
	    applet.graphPanel.repaint();

	    applet.dataPanel.repaint();

	    startButton.setLabel(STARTSTRING);
	    pauseButton.setLabel(PAUSESTRING);
	    startButton.enable();
	    pauseButton.disable();

/* set the status label to the null string */
	    applet.statusPanel.setText("");

	} else if (e.target instanceof Button && (STARTSTRING.equals((String)o))) {

	    applet.graphPanel.initialize(); /* reset the histogram */
	    applet.graphPanel.makeReady();
	    applet.graphPanel.thread.resume();

	    startButton.setLabel(STOPSTRING);
	    pauseButton.enable();
	    distributionChoice.disable();
	    applet.statusPanel.setText(StatusPanel.RUNNINGSTRING);

	} else if (e.target instanceof Button && (PAUSESTRING.equals((String)o))) {

	    applet.graphPanel.makeNotReady();
	    pauseButton.setLabel(RESUMESTRING);
	    applet.statusPanel.setText(StatusPanel.PAUSEDSTRING);

	} else if (e.target instanceof Button && (RESUMESTRING.equals((String)o))) {

	    pauseButton.setLabel(PAUSESTRING);
	    applet.statusPanel.setText(StatusPanel.RUNNINGSTRING);
	    applet.graphPanel.makeReady();
	    applet.graphPanel.thread.resume();

	} else if (e.target instanceof Button && (STOPSTRING.equals((String)o))) {

	    applet.graphPanel.makeNotReady();
	    reset(StatusPanel.NULLSTRING);
	}
	repaint();
	return(true);
    }

    public void reset(String status) {
	startButton.setLabel(STARTSTRING);
	pauseButton.setLabel(PAUSESTRING);
	startButton.enable();
	pauseButton.disable();
	distributionChoice.enable();
	if (applet.statusPanel != null)
	    applet.statusPanel.setText(status);
	repaint();
    }
}

class DataPanel extends Panel {
    public final static String SAMPLESIZESTRING = "Size: ";
    public final static String MEANSTRING = "Mean: ";
    public final static String VARIANCESTRING = "Variance: ";

    public final static Font DATAFONT = new Font("Dialog", Font.PLAIN, 10);

    SamplingApplet applet;
    Image offI;
    Graphics offG;

    int xOfs = 5;
    int yOfs = 10;
    int fontHeight = 10;
    int gutter = 5;
    boolean initialized = false;

    public DataPanel(SamplingApplet applet) {
	this.applet = applet;
    }

    public void paint(Graphics g) {
	Dimension d = size();
	int sampleSize = applet.graphPanel.getSampleSize();
	double sum = applet.graphPanel.getSum();
	double sum2 = applet.graphPanel.getSum2();
	double variance = 0.0;

	if (!initialized) {
	    initialized = true;
	    offI = createImage(d.width, d.height);
	    offG = offI.getGraphics();
	}

	if (sampleSize > 0)
	    variance = ((double)sampleSize*sum2 - sum*sum)/(double)(sampleSize*(sampleSize-1));

	offG.setColor(SamplingApplet.BACKGROUNDCOLOR);
	offG.fill3DRect(0, 0, d.width-1, d.height-1, true);
	offG.setColor(Color.blue);
	offG.drawString(SAMPLESIZESTRING + sampleSize, xOfs, yOfs);
	offG.drawString(MEANSTRING + sum/(double)sampleSize, xOfs, yOfs+fontHeight+gutter);
	offG.drawString(VARIANCESTRING + variance, xOfs, yOfs+2*(fontHeight+gutter));

	g.drawImage(offI, 0, 0, this);
    }
}

class GraphPanel extends Panel implements Runnable {
    int current = 0;
    SamplingApplet applet;
    Thread thread;
    Distribution dist[];
    boolean running = false;
    boolean readyToPaint = true;
    
    public GraphPanel(SamplingApplet applet) {
	this.applet = applet;
    }

    public void start() {
	if (thread == null) {
	    dist = new Distribution[applet.distributionNames.length];
	    for (int i=0; i<applet.distributionNames.length; i++) {
		try {
		    Class c = Class.forName(applet.distributionNames[i]);
		    dist[i] = (Distribution)(c.newInstance());
		    dist[i].setArgs(applet, size());
		    dist[i].initialize();
		} catch (Exception e) {}
	    }

	    thread = new Thread(this);
	    thread.start();
	}
    }

    public void stop() {
	thread = null;
    }

    public void run() {
	while (thread != null) {
	    if (!running) {
		repaint();
		thread.suspend();
	    }
	    repaint();
	    applet.dataPanel.repaint();
	    try { thread.sleep(Distribution.NAPTIME); } catch (Exception e) { };
	    readyToPaint = false;
	    dist[current].sample();
	    readyToPaint = true;
	    if (dist[current].completed()) {
		makeNotReady();
		applet.controlPanel.reset(StatusPanel.COMPLETEDSTRING);
	    }
	}
    }

    public synchronized void makeReady() {
	running = true;
    }

    public synchronized void makeNotReady() {
	running = false;
    }

/* some helper methods */
    public void initialize() {
	readyToPaint = true;
	dist[current].initialize();
    }

    public int getSampleSize() {
	return(dist[current].sampleSize);
    }

    public double getSum() {
	return(dist[current].sum);
    }

    public double getSum2() {
	return(dist[current].sum2);
    }

/* overriding update() reduces flicker */
    public void update(Graphics g) {
	paint(g);
    }

    public void paint(Graphics g) {
	if (!readyToPaint)
	    return;

	/* draw the current distribution's buffer */
	if (dist[current].offG != null)
	    g.drawImage(dist[current].offI, 0, 0, null);
    }
}

class StatusPanel extends Label {
    public final static String RUNNINGSTRING = "Running...";
    public final static String PAUSEDSTRING = "Paused...";
    public final static String COMPLETEDSTRING = "Completed...";
    public final static String NULLSTRING = "";

    public final static Font LABELFONT = new Font("Dialog", Font.PLAIN, 10);

    SamplingApplet applet;
    
    public StatusPanel(SamplingApplet applet) {
	this.applet = applet;
	setFont(LABELFONT);
    }
}

/**
  An abstract distribution class, that declares the methods that all
  subtypes must implement.
 */
abstract class Distribution {

    public static final int NAPTIME=50;

/* The axes, pdf are computed once and plotted into a static image (staticI).
   The sample data is plotted into a background image and copied into the graphPanel's gc
   to avoid flicker.
 */
    Image staticI = null; /* portions that do not change */
    Graphics staticG;
    Image offI;		/* the offscreen image */
    Graphics offG;

    double sum;
    double sum2;
    int sampleSize;

/* All specific distributions define these for data manipulation */
    abstract void setArgs(SamplingApplet a, Dimension d);
    abstract void initialize();
    abstract boolean completed();
    abstract void sample();
    abstract void plotPDF(Graphics g);
    abstract void plotAxes(Graphics g);
    abstract void plotHist(Graphics g);
    abstract void plotDistMean(Graphics g);
    abstract void plotSampleMean(Graphics g);
}

/**
  The unit Gaussian(0,1) or Normal distribution
 */
class Gaussian extends Distribution {
    SamplingApplet applet;

    int x;
    int y;
    int w;
    int h;

    double low;
    double high;
    double plotInterval;
    int numIntervals;
    int hist[];
    double intervalLength;
    double mean;		/* population mean */
    double variance;		/* population variance */

    int maxFreq = 100;
    Random rand;
    static final double c = 1.0/(Math.sqrt(2.0*Math.PI));

/* Sets some parameters */
    public void setArgs(SamplingApplet applet, Dimension d) {
	this.applet = applet;
	this.x = 0;
	this.y = 0;
	this.w = d.width;
	this.h = d.height;

/* compute some variables */
	low = -3.0;
	high = 3.0;
	mean = 0.0;
	variance = 1.0;
	plotInterval = 0.05;	/* for plotting the PDF */
	sampleSize = 0;
	numIntervals = 12;
	intervalLength = (high-low)/(double)(numIntervals);
    }

/* initializes background graphics, compute distributions etc. */
    public void initialize() {
	if (hist == null)
	    hist = new int[numIntervals];

/* clear accumulated data */
	clearHist();
	sampleSize = 0;
	sum = 0.0;
	sum2 = 0.0;

	rand = new Random((long)System.currentTimeMillis());

/* should only need to do this the first time around */
	if (staticI == null) {
	    staticI = applet.createImage(w, h);
	    staticG = staticI.getGraphics();
	    staticG.setColor(SamplingApplet.BACKGROUNDCOLOR);
	    staticG.fill3DRect(x, y, w-1, h-1, true);
	    plotAxes(staticG);
	    plotPDF(staticG);
	    plotDistMean(staticG);
	}
	offI = applet.createImage(w, h);
	offG = offI.getGraphics();
	offG.drawImage(staticI, 0, 0, null);
    }

/* clears the histogram array */
    public void clearHist() {
	if (hist != null) {
	    for (int i=0; i<hist.length; i++)
		hist[i] = 0;
	}
    }

/* terminating condition - when a cell has reached a maximum frequency */
    public boolean completed() {
	for (int i=0; i<hist.length; i++) {
	    if (hist[i] >= maxFreq)
		return(true);
	}
	return(false);
    }

/* generates a sample and adds to the histogram */
    public void sample() {
	double d = rand.nextGaussian();
	int i = (int)((d-low)/intervalLength);
	if (i>0 && i<numIntervals) {
	    hist[i]++;
	    sampleSize++;
	    sum += d;
	    sum2 += d*d;
	}

/* clear the offscreen graphics and plot the current histogram */
	offG.drawImage(staticI, 0, 0, null);
	plotHist(offG);
	plotSampleMean(offG);
    }

/* x axis is plotted at y=3/4h, from x=w/8 to x=7/8w; y axis at x=w/2 from
   y=h/8 to y=3/4h; x tics every w/16
   */
    public void plotAxes(Graphics g) {
	int tickHeight = 3;

	g.setColor(Color.black);

/* draw axes */
	g.drawLine(w/8, (int)((double)h*3/4), (int)((double)w*7/8), (int)((double)h*3/4));
	g.drawLine(w/8+(int)((double)w*3/8), h/8,
		   w/8+(int)((double)w*3/8), (int)((double)h*3/4)); /* y axis */
/* draw tics */
	for (int i=0; i<=12; i++) {
	    g.drawLine((int)w/8+(int)(i*(double)w/16), (int)((double)h*3/4),
		       (int)w/8+(int)(i*(double)w/16), (int)((double)h*3/4)-tickHeight);
	}
	for (int i=0; i<=5; i++) {
	    g.drawLine(w/8+(int)((double)w*3/8)-2,
		       (int)((double)h*3/4)-(int)(i*(double)h/8),
		       w/8+(int)((double)w*3/8)+2,
		       (int)((double)h*3/4)-(int)(i*(double)h/8));
	}
/* draw labels */
	g.setFont(new Font("Helvetica", Font.PLAIN, 10));
	double d = -3.0;
	for (int i=0; i<=6; i++) {
	    Double dObj = new Double(d);
	    int sw = g.getFontMetrics().stringWidth(dObj.toString());
	    g.drawString(dObj.toString(), (int)w/8+(int)(i*(double)w/8)-sw/2,
			 (int)((double)h*7/8)-10);
	    d += 1.0;
	}
	Integer iObj = new Integer(maxFreq);
	int sw = g.getFontMetrics().stringWidth(iObj.toString());
	g.drawString(iObj.toString(), (int)w/8+(int)((double)w*3/8)-sw/2,
		     (int)((double)h/8)-8);
    }

/* computes the PDF */
    public double pdf(double x) {
	return(c*Math.exp(-(x*x/2.0))); /* 1/2*pi (exp(-x*x/2)) */
    }

/* returns a scaled value suitable for plotting */
    public int scale(double val, double max, int maxXY) {
	return((int)((double)maxXY/max*val));
    }

/* overlays the probability density function */
    public void plotPDF(Graphics g) {
	double d1;
	double d2;
	int xo = w/2;
	int yo = (int)((double)h*3/4);

	d1 = d2 = low;
	d2 += plotInterval;

	g.setColor(Color.red);
	while (d1 < 0.0) {
	    int sx1 = scale(d1, (high-low), (int)((double)w*3/4));
	    int sx2 = scale(d2, (high-low), (int)((double)w*3/4));
	    int sy1 = scale(pdf(d1), c, (int)((double)h*5/8));
	    int sy2 = scale(pdf(d2), c, (int)((double)h*5/8));

	    g.drawLine(xo+sx1, yo-sy1, xo+sx2, yo-sy2);
	    g.drawLine(xo-sx1, yo-sy1, xo-sx2, yo-sy2);

	    d1 = d2;
	    d2 += plotInterval;
	}
    }

    public void plotDistMean(Graphics g) {
	g.setColor(Color.red);
	g.drawLine(w/8+(int)((double)w*3/8), h/8,
		   w/8+(int)((double)w*3/8), (int)((double)h*3/4));
    }

    public void plotSampleMean(Graphics g) {
	int x0 = w/2;
	int x1 = scale(sum/(double)sampleSize, high-low, (int)((double)w*3/4));
	int y1 = h/8;
	int y2 = (int)((double)h*3/4);

	g.setColor(Color.blue);
	g.drawLine(x0+x1, y1, x0+x1, y2);
    }

/* plots the current histogram */
    public void plotHist(Graphics g) {
	g.setColor(Color.black);
	for (int i=0; i<numIntervals; i++) {
	    int x1 = w/8+(int)(i*(double)w/16);
	    int y1 = (int)((double)h*3/4);
	    int x2 = w/8+(int)((i+1)*(double)w/16);
	    int y2 = (int)(((double)h*3/4)-((double)(hist[i])*h*5/(8*(double)maxFreq)));

	    g.drawRect(x1, y2, x2-x1, y1-y2);
	}
    }
}

/**
  The unit exponential(1) distribution
  */
class Exponential extends Distribution {
    SamplingApplet applet;

    int x;
    int y;
    int w;
    int h;

    double low;
    double high;
    double plotInterval;
    int numIntervals;
    int hist[];
    double intervalLength;
    double mean;
    double variance;

    int maxFreq = 100;
    Random rand;

/* Sets some parameters */
    public void setArgs(SamplingApplet applet, Dimension d) {
	this.applet = applet;
	this.x = 0;
	this.y = 0;
	this.w = d.width;
	this.h = d.height;

/* compute some variables */
	low = 0.0;
	high = 8.0;
	mean = 1.0;
	variance = 1.0;
	plotInterval = 0.1;	/* for plotting the PDF */
	sampleSize = 0;
	numIntervals = 16;
	intervalLength = (high-low)/(double)(numIntervals);
    }

/* initializes background graphics, compute distributions etc. */
    public void initialize() {
	if (hist == null)
	    hist = new int[numIntervals];

/* clear accumulated data */
	clearHist();
	sampleSize = 0;
	sum = 0;
	sum2 = 0;

	rand = new Random((long)System.currentTimeMillis());

/* should only need to do this the first time around */
	if (staticI == null) {
	    staticI = applet.createImage(w, h);
	    staticG = staticI.getGraphics();
	    staticG.setColor(SamplingApplet.BACKGROUNDCOLOR);
	    staticG.fill3DRect(x, y, w-1, h-1, true);
	    plotAxes(staticG);
	    plotPDF(staticG);
	    plotDistMean(staticG);
	}
	offI = applet.createImage(w, h);
	offG = offI.getGraphics();
	offG.drawImage(staticI, 0, 0, null);
    }

/* clears the histogram array */
    public void clearHist() {
	if (hist != null) {
	    for (int i=0; i<hist.length; i++)
		hist[i] = 0;
	}
    }

/* terminating condition - when a cell has reached a maximum frequency */
    public boolean completed() {
	for (int i=0; i<hist.length; i++) {
	    if (hist[i] >= maxFreq)
		return(true);
	}
	return(false);
    }

/* generates a sample and adds to the histogram */
    public void sample() {
	double d = invpdf(rand.nextDouble());
	int i = (int)((d-low)/intervalLength);
	if (i>=0 && i<numIntervals) {
	    hist[i]++;
	    sampleSize++;
	    sum += d;
	    sum2 += d*d;
	}

/* clear the offscreen graphics and plot the current histogram */
	offG.drawImage(staticI, 0, 0, null);
	plotHist(offG);
	plotSampleMean(offG);
    }

/* x-axis is plotted at y=3/4h, from x=w/6 to x=5/6w; y axes at x=w/6 from
   y=h/8 to y=3/4h; x tics at w/24
   */
    public void plotAxes(Graphics g) {
	int tickHeight = 3;

	g.setColor(Color.black);

/* axes */
	g.drawLine(w/6, (int)((double)h*3/4), (int)((double)w*5/6), (int)((double)h*3/4));
	g.drawLine(w/6, h/8, w/6, (int)((double)h*3/4)); /* y axis */

/* tics */
	for (int i=0; i<=16; i++) {
	    g.drawLine((int)((double)w/6)+(int)(i*(double)w/24),
		       (int)((double)h*3/4),
		       (int)((double)w/6)+(int)(i*(double)w/24),
		       (int)((double)h*3/4)-tickHeight);
	}
	for (int i=1; i<=5; i++) {
	    g.drawLine((int)((double)w/6)-2,
		       (int)((double)h*3/4)-(int)(i*(double)h/8),
		       (int)((double)w/6)+2,
		       (int)((double)h*3/4)-(int)(i*(double)h/8));
	}
/* labels */
	g.setFont(new Font("Helvetica", Font.PLAIN, 10));
	double d = 0.0;
	for (int i=0; i<=8; i++) {
	    Double dObj = new Double(d);
	    int sw = g.getFontMetrics().stringWidth(dObj.toString());
	    g.drawString(dObj.toString(), (int)w/6+(int)(i*(double)w/12)-sw/2,
			 (int)((double)h*7/8)-10);
	    d += 1.0;
	}
	int n = 0;
	for (int i=0; i<=5; i++) {
	    Integer iObj = new Integer(n);
	    int sw = g.getFontMetrics().stringWidth(iObj.toString());
	    g.drawString(iObj.toString(), (int)w/6-sw-5,
			 (int)((double)h*3/4)-(int)(i*(double)h/8)+5);
	    n += maxFreq/5;
	}
    }

/* computes the PDF */
    public double pdf(double x) {
	return(Math.exp(-x)); /* exp(-x) */
    }

/* computes the inverse PDF */
    public double invpdf(double x) {
	return((-1.0) * Math.log(x)); /* -ln(x) */
    }

/* returns a scaled value suitable for plotting */
    public int scale(double val, double max, int maxXY) {
	return((int)((double)maxXY/max*val));
    }

/* overlays the probability density function */
    public void plotPDF(Graphics g) {
	double d1;
	double d2;
	int xo = w/6;
	int yo = (int)((double)h*3/4);

	d1 = d2 = low;
	d2 += plotInterval;

	g.setColor(Color.red);
	while (d2 < high) {
	    int sx1 = scale(d1, (high-low), (int)((double)w*2/3));
	    int sx2 = scale(d2, (high-low), (int)((double)w*2/3));
	    int sy1 = scale(pdf(d1), 1.0, (int)((double)h*5/8));
	    int sy2 = scale(pdf(d2), 1.0, (int)((double)h*5/8));

	    g.drawLine(xo+sx1, yo-sy1, xo+sx2, yo-sy2);

	    d1 = d2;
	    d2 += plotInterval;
	}
    }

    public void plotDistMean(Graphics g) {
	g.setColor(Color.red);
	g.drawLine(w/6+w/12, h/8, w/6+w/12, (int)((double)h*3/4));
    }

    public void plotSampleMean(Graphics g) {
	int x0 = w/6;
	int x1 = scale(sum/(double)sampleSize, high-low, (int)((double)w*2/3));
	int y1 = h/8;
	int y2 = (int)((double)h*3/4);

	g.setColor(Color.blue);
	g.drawLine(x0+x1, y1, x0+x1, y2);
    }

    public void plotHist(Graphics g) {
	g.setColor(Color.black);
	for (int i=0; i<numIntervals; i++) {
	    int x1 = w/6+(int)(i*(double)w/24);
	    int y1 = (int)((double)h*3/4);
	    int x2 = w/6+(int)((i+1)*(double)w/24);
	    int y2 = (int)(((double)h*3/4)-((double)(hist[i])*h*5/(8*(double)maxFreq)));

	    g.drawRect(x1, y2, x2-x1, y1-y2);
	}
    }
}

/**
  The continuous uniform(0,1) distribution
  */
class Uniform extends Distribution {
    SamplingApplet applet;

    int x;
    int y;
    int w;
    int h;

    double low;
    double high;
    double plotInterval;
    int numIntervals;
    int hist[];
    double intervalLength;
    double mean;
    double variance;

    int maxFreq = 100;
    Random rand;

/* Sets some parameters */
    public void setArgs(SamplingApplet applet, Dimension d) {
	this.applet = applet;
	this.x = 0;
	this.y = 0;
	this.w = d.width;
	this.h = d.height;

/* compute some variables */
	low = 0.0;
	high = 1.0;
	mean = 0.5;
	variance = 1.0/12.0;	/* I think! */
	plotInterval = 0.1;	/* not used */
	sampleSize = 0;
	numIntervals = 10;
	intervalLength = (high-low)/(double)(numIntervals);
    }

/* initializes background graphics, compute distributions etc. */
    public void initialize() {
	if (hist == null)
	    hist = new int[numIntervals];

/* clear accumulated data */
	clearHist();
	sampleSize = 0;
	sum = 0;
	sum2 = 0;

	rand = new Random((long)System.currentTimeMillis());

/* should only need to do this the first time around */
	if (staticI == null) {
	    staticI = applet.createImage(w, h);
	    staticG = staticI.getGraphics();
	    staticG.setColor(SamplingApplet.BACKGROUNDCOLOR);
	    staticG.fill3DRect(x, y, w-1, h-1, true);
	    plotAxes(staticG);
	    plotPDF(staticG);
	    plotDistMean(staticG);
	}
	offI = applet.createImage(w, h);
	offG = offI.getGraphics();
	offG.drawImage(staticI, 0, 0, null);
    }

/* clears the histogram array */
    public void clearHist() {
	if (hist != null) {
	    for (int i=0; i<hist.length; i++)
		hist[i] = 0;
	}
    }

/* terminating condition - when a cell has reached a maximum frequency */
    public boolean completed() {
	for (int i=0; i<hist.length; i++) {
	    if (hist[i] >= maxFreq)
		return(true);
	}
	return(false);
    }

/* generates a sample and adds to the histogram */
    public void sample() {
	double d = rand.nextDouble();
	int i = (int)((d-low)/intervalLength);
	if (i>=0 && i<numIntervals) {
	    hist[i]++;
	    sampleSize++;
	    sum += d;
	    sum2 += d*d;
	}

/* clear the offscreen graphics and plot the current histogram */
	offG.drawImage(staticI, 0, 0, null);
	plotHist(offG);
	plotSampleMean(offG);
    }

/* x axis is plotted at y=3/4h, from x=w/7 to x=6/7w; y axis at x=w/7 from
   y=h/8 to y=3/4h; x-tics at w/14
   */
    public void plotAxes(Graphics g) {
	int tickHeight = 3;

	g.setColor(Color.black);

/* draw axes */
	g.drawLine(w/7, (int)((double)h*3/4), (int)((double)w*6/7), (int)((double)h*3/4));
	g.drawLine(w/7, h/8, w/7, (int)((double)h*3/4));

/* tics */
	for (int i=0; i<=10; i++) {
	    g.drawLine((int)((double)w/7)+(int)(i*(double)w/14),
		       (int)((double)h*3/4),
		       (int)((double)w/7)+(int)(i*(double)w/14),
		       (int)((double)h*3/4)-tickHeight);
	}
	for (int i=1; i<=5; i++) {
	    g.drawLine((int)((double)w/7)-2,
		       (int)((double)h*3/4)-(int)(i*(double)h/8),
		       (int)((double)w/7)+2,
		       (int)((double)h*3/4)-(int)(i*(double)h/8));
	}
/* labels */	
	g.setFont(new Font("Helvetica", Font.PLAIN, 10));
	double d = 0.0;
	for (int i=0; i<=5; i++) {
	    Double dObj = new Double(d);
	    int sw = g.getFontMetrics().stringWidth(dObj.toString());
	    g.drawString(dObj.toString(), (int)w/7+(int)(i*(double)w/7)-sw/2,
			 (int)((double)h*7/8)-10);
	    d += 0.2;
	}
	int n = 0;
	for (int i=0; i<=5; i++) {
	    Integer iObj = new Integer(n);
	    int sw = g.getFontMetrics().stringWidth(iObj.toString());
	    g.drawString(iObj.toString(), (int)w/7-sw-5,
			 (int)((double)h*3/4)-(int)(i*(double)h/8)+5);
	    n += maxFreq/5;
	}
    }

/* returns a scaled value suitable for plotting */
    public int scale(double val, double max, int maxXY) {
	return((int)((double)maxXY/max*val));
    }

    public void plotPDF(Graphics g) {
	g.setColor(Color.red);
	g.drawLine(w/7, (int)((double)h/8), (int)((double)w*6/7), (int)((double)h/8));
    }

    public void plotDistMean(Graphics g) {
	g.setColor(Color.red);
	g.drawLine(w/7+(int)((double)w*5/14), h/8, w/7+(int)((double)w*5/14),
		   (int)((double)h*3/4));
    }

    public void plotSampleMean(Graphics g) {
	int x0 = w/7;
	int x1 = scale(sum/(double)sampleSize, high-low, (int)((double)w*5/7));
	int y1 = h/8;
	int y2 = (int)((double)h*3/4);

	g.setColor(Color.blue);
	g.drawLine(x0+x1, y1, x0+x1, y2);
    }

    public void plotHist(Graphics g) {
	g.setColor(Color.black);
	for (int i=0; i<numIntervals; i++) {
	    int x1 = w/7+(int)(i*(double)w/14);
	    int y1 = (int)((double)h*3/4);
	    int x2 = w/7+(int)((i+1)*(double)w/14);
	    int y2 = (int)(((double)h*3/4)-((double)(hist[i])*h*5/(8*(double)maxFreq)));

	    g.drawRect(x1, y2, x2-x1, y1-y2);
	}
    }
}