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java.lang.Objectumontreal.iro.lecuyer.probdist.DiscreteDistributionInt
umontreal.iro.lecuyer.probdist.NegativeBinomialDist
public class NegativeBinomialDist
Extends the class DiscreteDistributionInt
for
the negative binomial distribution with real
parameters γ and p, where
γ > 0 and
0 <= p <= 1.
Its mass function is
If γ is an integer, p(x) can be interpreted as the probability
of having x failures before the γ-th success in a sequence of
independent Bernoulli trials with probability of success p. This special
case is implemented as the Pascal distribution (see PascalDist
).
Field Summary | |
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static double |
MAXN
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Fields inherited from class umontreal.iro.lecuyer.probdist.DiscreteDistributionInt |
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EPSILON |
Constructor Summary | |
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NegativeBinomialDist(double gamma,
double p)
Creates an object that contains the probability terms and the distribution function for the negative binomial distribution with parameters γ and p. |
Method Summary | |
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double |
barF(int x)
Returns bar(F)(x), the complementary distribution function. |
static double |
cdf(double gamma,
double p,
int x)
Computes the distribution function. |
double |
cdf(int x)
Returns the distribution function F evaluated at x (see). |
double |
getGamma()
Returns the parameter γ of this object. |
static NegativeBinomialDist |
getInstanceFromMLE(int[] x,
int n)
Creates a new instance of a negative binomial distribution with parameters γ and p estimated using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1. |
static NegativeBinomialDist |
getInstanceFromMLE(int[] x,
int n,
double gamma)
Creates a new instance of a negative binomial distribution with parameters γ = gamma given and hat(p) estimated using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1. |
static double[] |
getMaximumLikelihoodEstimate(int[] x,
int n)
Estimates and returns the parameters [ hat(γ), hat(p)] of the negative binomial distribution using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1. |
static double[] |
getMaximumLikelihoodEstimate(int[] x,
int n,
double gamma)
Estimates and returns the parameter [hat(p)] of the negative binomial distribution using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1. |
double |
getMean()
Returns the mean of the distribution function. |
static double |
getMean(double gamma,
double p)
Computes and returns the mean E[X] = γ(1 - p)/p of the negative binomial distribution with parameters γ and p. |
double |
getP()
Returns the parameter p of this object. |
double |
getStandardDeviation()
Returns the standard deviation of the distribution function. |
static double |
getStandardDeviation(double gamma,
double p)
Computes and returns the standard deviation of the negative binomial distribution with parameters γ and p. |
double |
getVariance()
Returns the variance of the distribution function. |
static double |
getVariance(double gamma,
double p)
Computes and returns the variance Var[X] = γ(1 - p)/p2 of the negative binomial distribution with parameters γ and p. |
static int |
inverseF(double gamma,
double p,
double u)
Computes the inverse function without precomputing tables. |
int |
inverseFInt(double u)
Returns the inverse distribution function F-1(u), where 0 <= u <= 1. |
static double |
prob(double gamma,
double p,
int x)
Computes the probability mass function. |
double |
prob(int x)
Returns p(x), the probability of x, which should be a real number in the interval [0, 1]. |
void |
setParams(double gamma,
double p)
Sets the parameter γ and p of this object. |
Methods inherited from class umontreal.iro.lecuyer.probdist.DiscreteDistributionInt |
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barF, cdf, inverseF |
Methods inherited from class java.lang.Object |
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equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Field Detail |
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public static double MAXN
Constructor Detail |
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public NegativeBinomialDist(double gamma, double p)
Method Detail |
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public double prob(int x)
DiscreteDistributionInt
prob
in class DiscreteDistributionInt
x
- value at which the mass function must be evaluated
public double cdf(int x)
DiscreteDistributionInt
cdf
in class DiscreteDistributionInt
x
- value at which the distribution function must be evaluated
public double barF(int x)
DiscreteDistributionInt
barF
in class DiscreteDistributionInt
x
- value at which the complementary distribution function
must be evaluated
public int inverseFInt(double u)
DiscreteDistributionInt
inverseFInt
in class DiscreteDistributionInt
u
- value in the interval (0, 1) for which
the inverse distribution function is evaluated
public double getMean()
Distribution
public double getVariance()
Distribution
public double getStandardDeviation()
Distribution
public static double prob(double gamma, double p, int x)
public static double cdf(double gamma, double p, int x)
public static int inverseF(double gamma, double p, double u)
public static NegativeBinomialDist getInstanceFromMLE(int[] x, int n, double gamma)
x
- the list of observations to use to evaluate parametersn
- the number of observations to use to evaluate parametersgamma
- the first parameter of the negative binomialpublic static double[] getMaximumLikelihoodEstimate(int[] x, int n, double gamma)
x
- the list of observations used to evaluate parametersn
- the number of observations used to evaluate parametersgamma
- the first parameter of the negative binomial
public static NegativeBinomialDist getInstanceFromMLE(int[] x, int n)
x
- the list of observations to use to evaluate parametersn
- the number of observations to use to evaluate parameterspublic static double[] getMaximumLikelihoodEstimate(int[] x, int n)
x
- the list of observations used to evaluate parametersn
- the number of observations used to evaluate parameters
public static double getMean(double gamma, double p)
public static double getVariance(double gamma, double p)
public static double getStandardDeviation(double gamma, double p)
public double getGamma()
public double getP()
public void setParams(double gamma, double p)
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