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java.lang.Objectumontreal.iro.lecuyer.probdist.DiscreteDistribution
public class DiscreteDistribution
Classes implementing discrete distributions over a
finite set of real numbers should inherit from this class.
For discrete distributions over integers,
see DiscreteDistributionInt
.
We assume that the random variable X of interest can take one of the
n values
x0 < ... < xn-1 (which are sorted by increasing order).
It takes the value xk with probability
pk = P[X = xk].
In addition to the methods specified in the interface
Distribution
,
a method that returns the probability pk is supplied.
Note that the default implementation of the complementary distribution function returns 1.0 - cdf(x - 1), which is not accurate when F(x) is near 1.
Constructor Summary | |
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DiscreteDistribution(int n,
double[] obs,
double[] prob)
Constructs a discrete distribution over the n values contained in array obs, with probabilities given in array prob. |
Method Summary | |
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double |
barF(double x)
Returns bar(F)(x) = 1 - F(x). |
double |
cdf(double x)
Computes and returns the distribution function F(x). |
double |
getMean()
Computes the mean E[X] = ∑i=1npixi of the distribution. |
double |
getStandardDeviation()
Computes the standard deviation of the distribution. |
double |
getVariance()
Computes the variance Var[X] = ∑i=1npi(xi - E[X])2 of the distribution. |
double |
inverseF(double u)
Computes and returns the inverse distribution function F-1(u), defined in. |
double |
prob(int k)
Returns pk, the probability of the k-th observation, for 0 <= k < n. |
Methods inherited from class java.lang.Object |
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equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Constructor Detail |
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public DiscreteDistribution(int n, double[] obs, double[] prob)
Method Detail |
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public double prob(int k)
k
- observation number,
0 <= k < n
public double cdf(double x)
Distribution
cdf
in interface Distribution
x
- value at which the distribution function must be evaluated
public double barF(double x)
Distribution
barF
in interface Distribution
x
- value at which the complementary distribution function must be evaluated
public double inverseF(double u)
Distribution
inverseF
in interface Distribution
u
- value in the interval (0, 1) for which the inverse
distribution function is evaluated
public double getMean()
getMean
in interface Distribution
public double getVariance()
getVariance
in interface Distribution
public double getStandardDeviation()
getStandardDeviation
in interface Distribution
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