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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 |
|---|
| Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
|---|
decPrec |
| Constructor Summary | |
|---|---|
NormalDist()
Constructs a NormalDist object with default parameters μ = 0 and σ = 1. |
|
NormalDist(double mu,
double sigma)
Constructs a NormalDist object with mean μ = mu and standard deviation σ = sigma. |
|
| Method Summary | |
|---|---|
double |
barF(double x)
Returns the complementary distribution function. |
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 σ2. |
static double |
barF01(double x)
Same as barF (0, 1, x). |
double |
cdf(double 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, 1, x). |
double |
density(double x)
Returns f (x), the density evaluated at x. |
static double |
density(double mu,
double sigma,
double x)
Computes the normal density function. |
static double |
density01(double x)
Same as density (0, 1, x). |
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 x[i], i = 0, 1,…, n - 1. |
double |
getMean()
Returns the mean. |
static double |
getMean(double mu,
double sigma)
Computes and returns the mean E[X] = μ of the normal distribution with parameters μ and σ. |
static double[] |
getMLE(double[] x,
int n)
Estimates the parameters (μ, σ) of the normal distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. |
double |
getMu()
Returns the parameter μ. |
double[] |
getParams()
Return a table containing the parameters of the current distribution. |
double |
getSigma()
Returns the parameter σ. |
double |
getStandardDeviation()
Returns the standard deviation. |
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. |
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)
Returns the inverse distribution function x = F-1(u). |
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, 1, u). |
void |
setParams(double mu,
double sigma)
Sets the parameters μ and σ of this object. |
String |
toString()
|
| Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution |
|---|
getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup |
| Methods inherited from class java.lang.Object |
|---|
equals, getClass, hashCode, notify, notifyAll, wait, wait, wait |
| Constructor Detail |
|---|
public NormalDist()
public NormalDist(double mu,
double sigma)
| Method Detail |
|---|
public double density(double x)
ContinuousDistribution
density in class ContinuousDistributionx - value at which the density is evaluated
public double cdf(double x)
Distribution
public double barF(double x)
ContinuousDistribution
barF in interface DistributionbarF in class ContinuousDistributionx - value at which the complementary distribution function is evaluated
public double inverseF(double u)
ContinuousDistribution
inverseF in interface DistributioninverseF in class ContinuousDistributionu - value at which the inverse distribution function is evaluated
public double getMean()
ContinuousDistribution
getMean in interface DistributiongetMean in class ContinuousDistributionpublic double getVariance()
ContinuousDistribution
getVariance in interface DistributiongetVariance in class ContinuousDistributionpublic double getStandardDeviation()
ContinuousDistribution
getStandardDeviation in interface DistributiongetStandardDeviation in class ContinuousDistributionpublic static double density01(double x)
density (0, 1, x).
public static double density(double mu,
double sigma,
double x)
public static double cdf01(double x)
cdf (0, 1, x).
public static double cdf(double mu,
double sigma,
double x)
public static double barF01(double x)
barF (0, 1, x).
public static double barF(double mu,
double sigma,
double x)
public static double inverseF01(double u)
inverseF (0, 1, u).
public static double inverseF(double mu,
double sigma,
double u)
public static double[] getMLE(double[] x,
int n)
x - the list of observations used to evaluate parametersn - the number of observations used to evaluate parameters
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 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)
public double[] getParams()
public String toString()
toString in class Object
|
SSJ V. labo. |
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| PREV CLASS NEXT CLASS | FRAMES NO FRAMES | ||||||||
| SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD | ||||||||