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java.lang.Objectumontreal.iro.lecuyer.probdist.ContinuousDistribution
umontreal.iro.lecuyer.probdist.NormalDist
public class NormalDist
Extends the class ContinuousDistribution
for the normal
distribution (e.g.,). It has mean μ
and variance σ2. Its density function is
cdf01
, barF01
,
and inverseF01
, respectively.
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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NormalDist()
Constructs a NormalDist object with default parameters μ = 0 and σ = 1. |
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NormalDist(double mu,
double sigma)
Constructs a NormalDist object with parameters μ = mu and σ = sigma. |
Method Summary | |
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double |
barF(double x)
Returns bar(F)(x) = 1 - F(x). |
static double |
barF(double mu,
double sigma,
double x)
Computes the complementary normal distribution function bar(F)(x) = 1 - Φ((x - μ)/σ), with mean μ and variance σ. |
static double |
barF01(double x)
Same as barF (0.0, 1.0, x). |
double |
cdf(double x)
Computes and returns the distribution function F(x). |
static double |
cdf(double mu,
double sigma,
double x)
Computes the normal distribution function with mean μ and variance σ2. |
static double |
cdf01(double x)
Same as cdf (0.0, 1.0, x). |
double |
density(double x)
Returns f (x), the density of X evaluated at x. |
static double |
density(double mu,
double sigma,
double x)
Computes the normal density function. |
static NormalDist |
getInstanceFromMLE(double[] x,
int n)
Creates a new instance of a normal distribution with parameters μ and σ estimated using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1. |
static double[] |
getMaximumLikelihoodEstimate(double[] x,
int n)
Estimates and returns the parameters [hat(μ), hat(σ)] of the normal 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 mu,
double sigma)
Computes and returns the mean E[X] = μ of the normal distribution with parameters μ and σ. |
double |
getMu()
Returns the parameter μ. |
double |
getSigma()
Returns the parameter σ. |
double |
getStandardDeviation()
Returns the standard deviation of the distribution function. |
static double |
getStandardDeviation(double mu,
double sigma)
Computes and returns the standard deviation σ of the normal distribution with parameters μ and σ. |
double |
getVariance()
Returns the variance of the distribution function. |
static double |
getVariance(double mu,
double sigma)
Computes and returns the variance Var[X] = σ2 of the normal distribution with parameters μ and σ. |
double |
inverseF(double u)
Computes and returns the inverse distribution function F-1(u), defined in. |
static double |
inverseF(double mu,
double sigma,
double u)
Computes the inverse normal distribution function with mean μ and variance σ2. |
static double |
inverseF01(double u)
Same as inverseF (0.0, 1.0, u). |
void |
setParams(double mu,
double sigma)
Sets the parameters μ and σ of this object. |
Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
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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 NormalDist()
public NormalDist(double mu, double sigma)
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 barF(double x)
Distribution
barF
in interface Distribution
barF
in class ContinuousDistribution
x
- value at which the complementary 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 mu, double sigma, double x)
public static double cdf01(double x)
cdf
(0.0, 1.0, x).
public static double cdf(double mu, double sigma, double x)
public static double barF01(double x)
barF
(0.0, 1.0, x).
public static double barF(double mu, double sigma, double x)
public static double inverseF01(double u)
inverseF
(0.0, 1.0, u).
public static double inverseF(double mu, double sigma, double u)
public static NormalDist 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 used to evaluate parametersn
- the number of observations used to evaluate parameters
public static double getMean(double mu, double sigma)
public static double getVariance(double mu, double sigma)
public static double getStandardDeviation(double mu, double sigma)
public double getMu()
public double getSigma()
public void setParams(double mu, double sigma)
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