* 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) Math.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
*/
public double cumulativeProbability(double x0, double x1)
throws MathException {
if (x0 > x1) {
throw new IllegalArgumentException
("lower endpoint must be less than or equal to upper endpoint");
}
if (Math.floor(x0) < x0) {
return cumulativeProbability(((int) Math.floor(x0)) + 1,
(int) Math.floor(x1)); // don't want to count mass below x0
} else { // x0 is mathematical integer, so use as is
return cumulativeProbability((int) Math.floor(x0),
(int) Math.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.
*/
abstract public 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 = Math.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 new IllegalArgumentException
("lower endpoint must be less than or equal to upper endpoint");
}
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 new IllegalArgumentException(
"p must be between 0 and 1.0 (inclusive)");
}
// 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 = cumulativeProbability(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 = cumulativeProbability(x0);
while (pm > p) {
--x0;
pm = cumulativeProbability(x0);
}
return x0;
}
/**
* 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);
}