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java.lang.Objectumontreal.iro.lecuyer.probdist.DiscreteDistributionInt
umontreal.iro.lecuyer.probdist.BinomialDist
public class BinomialDist
Extends the class DiscreteDistributionInt
for the
binomial distribution with parameters n and p, where
n is a positive integer and
0 <= p <= 1.
Its mass function is given by
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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BinomialDist(int n,
double p)
Creates an object that contains the binomial terms, for 0 <= x <= n, and the corresponding cumulative function. |
Method Summary | |
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double |
barF(int x)
Returns bar(F)(x), the complementary distribution function. |
double |
cdf(int x)
Returns the distribution function F evaluated at x (see). |
static double |
cdf(int n,
double p,
int x)
Computes F(x), the distribution function of a binomial random variable with parameters n and p, evaluated at x. |
static BinomialDist |
getInstanceFromMLE(int[] x,
int m)
Creates a new instance of a binomial distribution with both parameters hat(n) and hat(p) estimated using the maximum likelihood method based on the m observations x[i], i = 0, 1,…, m - 1. |
static BinomialDist |
getInstanceFromMLE(int[] x,
int m,
int n)
Creates a new instance of a binomial distribution with given parameter n and estimated parameter hat(p) using the maximum likelihood method based on the m observations in table x[i], i = 0, 1,…, m - 1. |
static double[] |
getMaximumLikelihoodEstimate(int[] x,
int m)
Estimates the parameters [hat(n), hat(p)] of the binomial distribution using the maximum likelihood method based on the m observations in table x[i], i = 0, 1,…, m - 1. |
static double[] |
getMaximumLikelihoodEstimate(int[] x,
int m,
int n)
Estimates the parameter [hat(p)] of the binomial distribution with given parameter n using the maximum likelihood method based on the m observations x[i], i = 0, 1,…, m - 1. |
double |
getMean()
Returns the mean of the distribution function. |
static double |
getMean(int n,
double p)
Computes the mean E[X] = np of the binomial distribution with parameters n and p. |
int |
getN()
Returns the parameter n of this object. |
double |
getP()
Returns the parameter p of this object. |
double |
getStandardDeviation()
Returns the standard deviation of the distribution function. |
static double |
getStandardDeviation(int n,
double p)
Computes the standard deviation of the Binomial distribution with parameters n and p. |
double |
getVariance()
Returns the variance of the distribution function. |
static double |
getVariance(int n,
double p)
Computes the variance Var[X] = np(1 - p) of the binomial distribution with parameters n and p. |
static int |
inverseF(int n,
double p,
double u)
Computes the inverse of the binomial distribution, x = F-1(u), using a linear search starting at the mode if n is small. |
int |
inverseFInt(double u)
Returns the inverse distribution function F-1(u), where 0 <= u <= 1. |
double |
prob(int x)
Returns p(x), the probability of x, which should be a real number in the interval [0, 1]. |
static double |
prob(int n,
double p,
double q,
int x)
A generalization of the previous method. |
static double |
prob(int n,
double p,
int x)
Computes and returns the mass function p(x). |
void |
setParams(int n,
double p)
Resets the parameters to these new values and recomputes everything as in the constructor. |
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 BinomialDist(int n, 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(int n, double p, int x)
public static double prob(int n, double p, double q, int x)
public static double cdf(int n, double p, int x)
public static int inverseF(int n, double p, double u)
cdf
static method is used to compute F(x) at
different values of x, which much is less efficient.
public static BinomialDist getInstanceFromMLE(int[] x, int m)
x
- the list of observations to use to evaluate parametersm
- the number of observations to use to evaluate parameterspublic static double[] getMaximumLikelihoodEstimate(int[] x, int m)
x
- the list of observations used to evaluate parametersm
- the number of observations used to evaluate parameters
public static BinomialDist getInstanceFromMLE(int[] x, int m, int n)
x
- the list of observations to use to evaluate parametersm
- the number of observations to use to evaluate parametersn
- the parameter n of the binomialpublic static double[] getMaximumLikelihoodEstimate(int[] x, int m, int n)
x
- the list of observations used to evaluate parametersm
- the number of observations used to evaluate parametersn
- the number of success
public static double getMean(int n, double p)
public static double getVariance(int n, double p)
public static double getStandardDeviation(int n, double p)
public int getN()
public double getP()
public void setParams(int n, double p)
BinomialDist
object.
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SSJ V. 1.2.5. |
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