* If x does not represent an integer value, the CDF is
* evaluated at the greatest integer less than x.
*
* @param x the value at which the distribution function is evaluated.
* @return cumulative probability that a random variable with this
* distribution takes a value less than or equal to x
* @throws MathException if the cumulative probability can not be
* computed due to convergence or other numerical errors.
*/
public double cumulativeProbability(double x) throws MathException {
return cumulativeProbability((int) FastMath.floor(x));
}
/**
* For a random variable X whose values are distributed according
* to this distribution, this method returns P(x0 ≤ X ≤ x1).
*
* @param x0 the (inclusive) lower bound
* @param x1 the (inclusive) upper bound
* @return the probability that a random variable with this distribution
* will take a value between x0 and x1,
* including the endpoints.
* @throws MathException if the cumulative probability can not be
* computed due to convergence or other numerical errors.
* @throws IllegalArgumentException if x0 > x1
*/
@Override
public double cumulativeProbability(double x0, double x1)
throws MathException {
if (x0 > x1) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT, x0, x1);
}
if (FastMath.floor(x0) < x0) {
return cumulativeProbability(((int) FastMath.floor(x0)) + 1,
(int) FastMath.floor(x1)); // don't want to count mass below x0
} else { // x0 is mathematical integer, so use as is
return cumulativeProbability((int) FastMath.floor(x0),
(int) FastMath.floor(x1));
}
}
/**
* For a random variable X whose values are distributed according
* to this distribution, this method returns P(X ≤ x). In other words,
* this method represents the probability distribution function, or PDF,
* for this distribution.
*
* @param x the value at which the PDF is evaluated.
* @return PDF for this distribution.
* @throws MathException if the cumulative probability can not be
* computed due to convergence or other numerical errors.
*/
public abstract double cumulativeProbability(int x) throws MathException;
/**
* For a random variable X whose values are distributed according
* to this distribution, this method returns P(X = x). In other words, this
* method represents the probability mass function, or PMF, for the distribution.
*
* If x does not represent an integer value, 0 is returned.
*
* @param x the value at which the probability density function is evaluated
* @return the value of the probability density function at x
*/
public double probability(double x) {
double fl = FastMath.floor(x);
if (fl == x) {
return this.probability((int) x);
} else {
return 0;
}
}
/**
* For a random variable X whose values are distributed according
* to this distribution, this method returns P(x0 ≤ X ≤ x1).
*
* @param x0 the inclusive, lower bound
* @param x1 the inclusive, upper bound
* @return the cumulative probability.
* @throws MathException if the cumulative probability can not be
* computed due to convergence or other numerical errors.
* @throws IllegalArgumentException if x0 > x1
*/
public double cumulativeProbability(int x0, int x1) throws MathException {
if (x0 > x1) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT, x0, x1);
}
return cumulativeProbability(x1) - cumulativeProbability(x0 - 1);
}
/**
* For a random variable X whose values are distributed according
* to this distribution, this method returns the largest x, such
* that P(X ≤ x) ≤ p.
*
* @param p the desired probability
* @return the largest x such that P(X ≤ x) <= p
* @throws MathException if the inverse cumulative probability can not be
* computed due to convergence or other numerical errors.
* @throws IllegalArgumentException if p < 0 or p > 1
*/
public int inverseCumulativeProbability(final double p) throws MathException{
if (p < 0.0 || p > 1.0) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.OUT_OF_RANGE_SIMPLE, p, 0.0, 1.0);
}
// by default, do simple bisection.
// subclasses can override if there is a better method.
int x0 = getDomainLowerBound(p);
int x1 = getDomainUpperBound(p);
double pm;
while (x0 < x1) {
int xm = x0 + (x1 - x0) / 2;
pm = checkedCumulativeProbability(xm);
if (pm > p) {
// update x1
if (xm == x1) {
// this can happen with integer division
// simply decrement x1
--x1;
} else {
// update x1 normally
x1 = xm;
}
} else {
// update x0
if (xm == x0) {
// this can happen with integer division
// simply increment x0
++x0;
} else {
// update x0 normally
x0 = xm;
}
}
}
// insure x0 is the correct critical point
pm = checkedCumulativeProbability(x0);
while (pm > p) {
--x0;
pm = checkedCumulativeProbability(x0);
}
return x0;
}
/**
* Reseeds the random generator used to generate samples.
*
* @param seed the new seed
* @since 2.2
*/
public void reseedRandomGenerator(long seed) {
randomData.reSeed(seed);
}
/**
* Generates a random value sampled from this distribution. The default
* implementation uses the
* inversion method.
*
* @return random value
* @since 2.2
* @throws MathException if an error occurs generating the random value
*/
public int sample() throws MathException {
return randomData.nextInversionDeviate(this);
}
/**
* Generates a random sample from the distribution. The default implementation
* generates the sample by calling {@link #sample()} in a loop.
*
* @param sampleSize number of random values to generate
* @since 2.2
* @return an array representing the random sample
* @throws MathException if an error occurs generating the sample
* @throws IllegalArgumentException if sampleSize is not positive
*/
public int[] sample(int sampleSize) throws MathException {
if (sampleSize <= 0) {
MathRuntimeException.createIllegalArgumentException(LocalizedFormats.NOT_POSITIVE_SAMPLE_SIZE, sampleSize);
}
int[] out = new int[sampleSize];
for (int i = 0; i < sampleSize; i++) {
out[i] = sample();
}
return out;
}
/**
* Computes the cumulative probability function and checks for NaN values returned.
* Throws MathException if the value is NaN. Rethrows any MathException encountered
* evaluating the cumulative probability function. Throws
* MathException if the cumulative probability function returns NaN.
*
* @param argument input value
* @return cumulative probability
* @throws MathException if the cumulative probability is NaN
*/
private double checkedCumulativeProbability(int argument) throws MathException {
double result = Double.NaN;
result = cumulativeProbability(argument);
if (Double.isNaN(result)) {
throw new MathException(LocalizedFormats.DISCRETE_CUMULATIVE_PROBABILITY_RETURNED_NAN, argument);
}
return result;
}
/**
* Access the domain value lower bound, based on p, used to
* bracket a PDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return domain value lower bound, i.e.
* P(X < lower bound) < p
*/
protected abstract int getDomainLowerBound(double p);
/**
* Access the domain value upper bound, based on p, used to
* bracket a PDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @param p the desired probability for the critical value
* @return domain value upper bound, i.e.
* P(X < upper bound) > p
*/
protected abstract int getDomainUpperBound(double p);
/**
* Use this method to get information about whether the lower bound
* of the support is inclusive or not. For discrete support,
* only true here is meaningful.
*
* @return true (always but at Integer.MIN_VALUE because of the nature of discrete support)
* @since 2.2
*/
public boolean isSupportLowerBoundInclusive() {
return true;
}
/**
* Use this method to get information about whether the upper bound
* of the support is inclusive or not. For discrete support,
* only true here is meaningful.
*
* @return true (always but at Integer.MAX_VALUE because of the nature of discrete support)
* @since 2.2
*/
public boolean isSupportUpperBoundInclusive() {
return true;
}
}