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java.lang.Objectumontreal.iro.lecuyer.probdist.ContinuousDistribution
umontreal.iro.lecuyer.probdist.GammaDist
public class GammaDist
Extends the class ContinuousDistribution
for
the gamma distribution with
shape parameter
α > 0 and scale parameter
λ > 0.
The density is
Field Summary |
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Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
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decPrec |
Constructor Summary | |
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GammaDist(double alpha)
Constructs a GammaDist object with parameters α = alpha and λ = 1. |
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GammaDist(double alpha,
double lambda)
Constructs a GammaDist object with parameters α = alpha and λ = lambda. |
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GammaDist(double alpha,
double lambda,
int d)
Constructs a GammaDist object with parameters α = alpha and λ = lambda, and approximations of roughly d decimal digits of precision when computing functions. |
Method Summary | |
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static double |
barF(double alpha,
double lambda,
int d,
double x)
Computes the complementary distribution function. |
static double |
barF(double alpha,
int d,
double x)
Same as barF (alpha, 1.0, d, x). |
double |
cdf(double x)
Computes and returns the distribution function F(x). |
static double |
cdf(double alpha,
double lambda,
int d,
double x)
Returns an approximation of the gamma distribution function with parameters α = alpha and λ = lambda. |
static double |
cdf(double alpha,
int d,
double x)
Equivalent to cdf (alpha, 1.0, d, x). |
double |
density(double x)
Returns f (x), the density of X evaluated at x. |
static double |
density(double alpha,
double lambda,
double x)
Computes the density function. |
double |
getAlpha()
Return the parameter α for this object. |
static GammaDist |
getInstanceFromMLE(double[] x,
int n)
Creates a new instance of a gamma distribution with parameters α and λ estimated using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1. |
double |
getLambda()
Return the parameter λ for this object. |
static double[] |
getMaximumLikelihoodEstimate(double[] x,
int n)
Estimates and returns the parameters [ hat(α), hat(λ)] of the gamma 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 alpha,
double lambda)
Computes and returns the mean E[X] = α/λ of the gamma distribution with parameters α and λ. |
double |
getStandardDeviation()
Returns the standard deviation of the distribution function. |
static double |
getStandardDeviation(double alpha,
double lambda)
Computes and returns the standard deviation of the gamma distribution with parameters α and λ. |
double |
getVariance()
Returns the variance of the distribution function. |
static double |
getVariance(double alpha,
double lambda)
Computes and returns the variance Var[X] = α/λ2 of the gamma distribution with parameters α and λ. |
double |
inverseF(double u)
Computes and returns the inverse distribution function F-1(u), defined in. |
static double |
inverseF(double alpha,
double lambda,
int d,
double u)
Computes the inverse distribution function using the algorithm implemented in the Cephes Math Library. |
static double |
inverseF(double alpha,
int d,
double u)
Same as inverseF (alpha, 1, d, u). |
void |
setParams(double alpha,
double lambda,
int d)
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Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
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barF, inverseBisection, inverseBrent |
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 GammaDist(double alpha)
public GammaDist(double alpha, double lambda)
public GammaDist(double alpha, double lambda, int d)
Method Detail |
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public double density(double x)
ContinuousDistribution
density
in class ContinuousDistribution
x
- value at which the density is evaluated
public double cdf(double x)
Distribution
x
- value at which the distribution function is evaluated
public double inverseF(double u)
Distribution
inverseF
in interface Distribution
inverseF
in class ContinuousDistribution
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 density(double alpha, double lambda, double x)
public static double cdf(double alpha, double lambda, int d, double x)
public static double cdf(double alpha, int d, double x)
public static double barF(double alpha, double lambda, int d, double x)
public static double barF(double alpha, int d, double x)
barF
(alpha, 1.0, d, x).
public static double inverseF(double alpha, double lambda, int d, double u)
barF
function. The argument d
gives a good idea of the precision attained.
public static double inverseF(double alpha, int d, double u)
inverseF
(alpha, 1, d, u).
public static GammaDist getInstanceFromMLE(double[] 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(double[] x, int n)
x
- the list of observations to use to evaluate parametersn
- the number of observations to use to evaluate parameters
public static double getMean(double alpha, double lambda)
public static double getVariance(double alpha, double lambda)
public static double getStandardDeviation(double alpha, double lambda)
public double getAlpha()
public double getLambda()
public void setParams(double alpha, double lambda, int d)
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