NormalDistribution (nd4j-api 0.0.3.5.5.5 API)

java.lang.Object
- org.nd4j.linalg.api.rng.distribution.BaseDistribution
- - org.nd4j.linalg.api.rng.distribution.impl.NormalDistribution

All Implemented Interfaces:

Distribution
```
public class NormalDistribution
extends BaseDistribution
```
Base distribution derived from apache commons math http://commons.apache.org/proper/commons-math/
(specifically the org.apache.commons.math3.distribution.NormalDistribution

Author:

Adam Gibson

Field Summary

Fields
Modifier and Type Field and Description

static double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
Default inverse cumulative probability accuracy.
- Fields inherited from class org.nd4j.linalg.api.rng.distribution.BaseDistribution
  random

Fields
Modifier and Type	Field and Description
`static double`	`DEFAULT_INVERSE_ABSOLUTE_ACCURACY` Default inverse cumulative probability accuracy.

Constructor Summary

Constructors
Constructor and Description
`NormalDistribution()` Create a normal distribution with mean equal to zero and standard deviation equal to one.
`NormalDistribution(double mean, double sd)` Create a normal distribution using the given mean and standard deviation.
`NormalDistribution(double mean, double sd, double inverseCumAccuracy)` Create a normal distribution using the given mean, standard deviation and inverse cumulative distribution accuracy.
`NormalDistribution(double standardDeviation, INDArray means)`
`NormalDistribution(INDArray mean, double std)`
`NormalDistribution(Random rng, double mean, double sd, double inverseCumAccuracy)` Creates a normal distribution.
`NormalDistribution(Random rng, double standardDeviation, INDArray means)`

Method Summary

All Methods Instance Methods Concrete Methods Deprecated Methods
Modifier and Type	Method and Description
`double`	`cumulativeProbability(double x)` For a random variable `X` whose values are distributed according to this distribution, this method returns `P(X <= x)`.
`double`	`cumulativeProbability(double x0, double x1)` Deprecated. See `org.apache.commons.math3.distribution.RealDistribution#cumulativeProbability(double, double)`
`double`	`density(double x)` Returns the probability density function (PDF) of this distribution evaluated at the specified point `x`.
`double`	`getMean()` Access the mean.
`double`	`getNumericalMean()` Use this method to get the numerical value of the mean of this distribution.
`double`	`getNumericalVariance()` Use this method to get the numerical value of the variance of this distribution.
`protected double`	`getSolverAbsoluteAccuracy()` Returns the solver absolute accuracy for inverse cumulative computation.
`double`	`getStandardDeviation()` Access the standard deviation.
`double`	`getSupportLowerBound()` Access the lower bound of the support.
`double`	`getSupportUpperBound()` Access the upper bound of the support.
`double`	`inverseCumulativeProbability(double p)` Computes the quantile function of this distribution.
`boolean`	`isSupportConnected()` Use this method to get information about whether the support is connected, i.e.
`boolean`	`isSupportLowerBoundInclusive()` Whether or not the lower bound of support is in the domain of the density function.
`boolean`	`isSupportUpperBoundInclusive()` Whether or not the upper bound of support is in the domain of the density function.
`double`	`probability(double x0, double x1)` For a random variable `X` whose values are distributed according to this distribution, this method returns `P(x0 < X <= x1)`.
`double`	`sample()` Generate a random value sampled from this distribution.
`INDArray`	`sample(int[] shape)` Sample the given shape

Methods inherited from class org.nd4j.linalg.api.rng.distribution.BaseDistribution
probability, reseedRandomGenerator, sample

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - DEFAULT_INVERSE_ABSOLUTE_ACCURACY
```
public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
```
    Default inverse cumulative probability accuracy.
    
    Since:
    
    2.1
    
    See Also:
    
    Constant Field Values
- Constructor Detail
  - NormalDistribution
```
public NormalDistribution(Random rng,
                          double standardDeviation,
                          INDArray means)
```
  - NormalDistribution
```
public NormalDistribution(double standardDeviation,
                          INDArray means)
```
  - NormalDistribution
```
public NormalDistribution()
```
    Create a normal distribution with mean equal to zero and standard deviation equal to one.
  - NormalDistribution
```
public NormalDistribution(double mean,
                          double sd)
                   throws org.apache.commons.math3.exception.NotStrictlyPositiveException
```
    Create a normal distribution using the given mean and standard deviation.
    
    Parameters:
    
    mean - Mean for this distribution.
    
    sd - Standard deviation for this distribution.
    
    Throws:
    
    org.apache.commons.math3.exception.NotStrictlyPositiveException - if sd <= 0.
  - NormalDistribution
```
public NormalDistribution(double mean,
                          double sd,
                          double inverseCumAccuracy)
                   throws org.apache.commons.math3.exception.NotStrictlyPositiveException
```
    Create a normal distribution using the given mean, standard deviation and inverse cumulative distribution accuracy.
    
    Parameters:
    
    mean - Mean for this distribution.
    
    sd - Standard deviation for this distribution.
    
    inverseCumAccuracy - Inverse cumulative probability accuracy.
    
    Throws:
    
    org.apache.commons.math3.exception.NotStrictlyPositiveException - if sd <= 0.
    
    Since:
    
    2.1
  - NormalDistribution
```
public NormalDistribution(Random rng,
                          double mean,
                          double sd,
                          double inverseCumAccuracy)
                   throws org.apache.commons.math3.exception.NotStrictlyPositiveException
```
    Creates a normal distribution.
    
    Parameters:
    
    rng - Random number generator.
    
    mean - Mean for this distribution.
    
    sd - Standard deviation for this distribution.
    
    inverseCumAccuracy - Inverse cumulative probability accuracy.
    
    Throws:
    
    org.apache.commons.math3.exception.NotStrictlyPositiveException - if sd <= 0.
    
    Since:
    
    3.1
  - NormalDistribution
```
public NormalDistribution(INDArray mean,
                          double std)
```
- Method Detail
  - getMean
```
public double getMean()
```
    Access the mean.
    
    Returns:
    
    the mean for this distribution.
  - getStandardDeviation
```
public double getStandardDeviation()
```
    Access the standard deviation.
    
    Returns:
    
    the standard deviation for this distribution.
  - density
```
public double density(double x)
```
    Returns the probability density function (PDF) of this distribution evaluated at the specified point x. In general, the PDF is the derivative of the CDF. If the derivative does not exist at x, then an appropriate replacement should be returned, e.g. Double.POSITIVE_INFINITY, Double.NaN, or the limit inferior or limit superior of the difference quotient.
    
    Parameters:
    
    x - the point at which the PDF is evaluated
    
    Returns:
    
    the value of the probability density function at point x
  - cumulativeProbability
```
public double cumulativeProbability(double x)
```
    For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x). In other words, this method represents the (cumulative) distribution function (CDF) for this distribution.
    If x is more than 40 standard deviations from the mean, 0 or 1 is returned, as in these cases the actual value is within Double.MIN_VALUE of 0 or 1.
    
    Parameters:
    
    x - the point at which the CDF is evaluated
    
    Returns:
    
    the probability that a random variable with this distribution takes a value less than or equal to x
  - inverseCumulativeProbability
```
public double inverseCumulativeProbability(double p)
                                    throws org.apache.commons.math3.exception.OutOfRangeException
```
    Computes the quantile function of this distribution. For a random variable X distributed according to this distribution, the returned value is
    - inf{x in R | P(X<=x) >= p} for 0 < p <= 1,
    - inf{x in R | P(X<=x) > 0} for p = 0.
    The default implementation returns
    - Distribution.getSupportLowerBound() for p = 0,
    - Distribution.getSupportUpperBound() for p = 1.
    Specified by:
    
    inverseCumulativeProbability in interface Distribution
    
    Overrides:
    
    inverseCumulativeProbability in class BaseDistribution
    
    Parameters:
    
    p - the cumulative probability
    
    Returns:
    
    the smallest p-quantile of this distribution (largest 0-quantile for p = 0)
    
    Throws:
    
    org.apache.commons.math3.exception.OutOfRangeException - if p < 0 or p > 1
    
    Since:
    
    3.2
  - cumulativeProbability
```
@Deprecated
public double cumulativeProbability(double x0,
                                                double x1)
                                         throws org.apache.commons.math3.exception.NumberIsTooLargeException
```
    Deprecated. See org.apache.commons.math3.distribution.RealDistribution#cumulativeProbability(double, double)
    
    For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).
    
    Parameters:
    
    x0 - the exclusive lower bound
    
    x1 - the inclusive upper bound
    
    Returns:
    
    the probability that a random variable with this distribution takes a value between x0 and x1, excluding the lower and including the upper endpoint
    
    Throws:
    
    org.apache.commons.math3.exception.NumberIsTooLargeException - if x0 > x1
  - probability
```
public double probability(double x0,
                          double x1)
                   throws org.apache.commons.math3.exception.NumberIsTooLargeException
```
    For a random variable X whose values are distributed according to this distribution, this method returns P(x0 < X <= x1).
    
    Overrides:
    
    probability in class BaseDistribution
    
    Parameters:
    
    x0 - Lower bound (excluded).
    
    x1 - Upper bound (included).
    
    Returns:
    
    the probability that a random variable with this distribution takes a value between x0 and x1, excluding the lower and including the upper endpoint.
    
    Throws:
    
    org.apache.commons.math3.exception.NumberIsTooLargeException - if x0 > x1.
    The default implementation uses the identity P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)
  - getSolverAbsoluteAccuracy
```
protected double getSolverAbsoluteAccuracy()
```
    Returns the solver absolute accuracy for inverse cumulative computation. You can override this method in order to use a Brent solver with an absolute accuracy different from the default.
    
    Overrides:
    
    getSolverAbsoluteAccuracy in class BaseDistribution
    
    Returns:
    
    the maximum absolute error in inverse cumulative probability estimates
  - getNumericalMean
```
public double getNumericalMean()
```
    Use this method to get the numerical value of the mean of this distribution.
    For mean parameter mu, the mean is mu.
    
    Returns:
    
    the mean or Double.NaN if it is not defined
  - getNumericalVariance
```
public double getNumericalVariance()
```
    Use this method to get the numerical value of the variance of this distribution.
    For standard deviation parameter s, the variance is s^2.
    
    Returns:
    
    the variance (possibly Double.POSITIVE_INFINITY as for certain cases in org.apache.commons.math3.distribution.TDistribution) or Double.NaN if it is not defined
  - getSupportLowerBound
```
public double getSupportLowerBound()
```
    Access the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0). In other words, this method must return
    inf {x in R | P(X <= x) > 0}.
    
    The lower bound of the support is always negative infinity no matter the parameters.
    
    Returns:
    
    lower bound of the support (always Double.NEGATIVE_INFINITY)
  - getSupportUpperBound
```
public double getSupportUpperBound()
```
    Access the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1). In other words, this method must return
    inf {x in R | P(X <= x) = 1}.
    
    The upper bound of the support is always positive infinity no matter the parameters.
    
    Returns:
    
    upper bound of the support (always Double.POSITIVE_INFINITY)
  - isSupportLowerBoundInclusive
```
public boolean isSupportLowerBoundInclusive()
```
    Whether or not the lower bound of support is in the domain of the density function. Returns true iff getSupporLowerBound() is finite and density(getSupportLowerBound()) returns a non-NaN, non-infinite value.
    
    Returns:
    
    true if the lower bound of support is finite and the density function returns a non-NaN, non-infinite value there
  - isSupportUpperBoundInclusive
```
public boolean isSupportUpperBoundInclusive()
```
    Whether or not the upper bound of support is in the domain of the density function. Returns true iff getSupportUpperBound() is finite and density(getSupportUpperBound()) returns a non-NaN, non-infinite value.
    
    Returns:
    
    true if the upper bound of support is finite and the density function returns a non-NaN, non-infinite value there
  - isSupportConnected
```
public boolean isSupportConnected()
```
    Use this method to get information about whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support.
    The support of this distribution is connected.
    
    Returns:
    
    true
  - sample
```
public double sample()
```
    Generate a random value sampled from this distribution.
    The default implementation uses the inversion method.
    
    Specified by:
    
    sample in interface Distribution
    
    Overrides:
    
    sample in class BaseDistribution
    
    Returns:
    
    a random value.
  - sample
```
public INDArray sample(int[] shape)
```
    Description copied from interface: Distribution
    
    Sample the given shape
    
    Specified by:
    
    sample in interface Distribution
    
    Overrides:
    
    sample in class BaseDistribution
    
    Parameters:
    
    shape - the given shape
    
    Returns:
    
    an ndarray with random samples from this distribution

Class NormalDistribution

Field Summary

Fields inherited from class org.nd4j.linalg.api.rng.distribution.BaseDistribution

Constructor Summary

Method Summary

Methods inherited from class org.nd4j.linalg.api.rng.distribution.BaseDistribution

Methods inherited from class java.lang.Object

Field Detail

DEFAULT_INVERSE_ABSOLUTE_ACCURACY

Constructor Detail

NormalDistribution

NormalDistribution

NormalDistribution

NormalDistribution

NormalDistribution

NormalDistribution

NormalDistribution

Method Detail

getMean

getStandardDeviation

density

cumulativeProbability

inverseCumulativeProbability

cumulativeProbability

probability

getSolverAbsoluteAccuracy

getNumericalMean

getNumericalVariance

getSupportLowerBound

getSupportUpperBound

isSupportLowerBoundInclusive

isSupportUpperBoundInclusive

isSupportConnected

sample

sample