Normal Distribution Class
Represents a normal distribution.
Definition
Namespace: Extreme.Statistics.Distributions
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23
C#
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23
[SerializableAttribute]
public class NormalDistribution : ContinuousDistribution
- Inheritance
- Object → Distribution → ContinuousDistribution → NormalDistribution
Remarks
Normal distributions are a family of distributions that have the same general shape. They are symmetric with outcomes more concentrated in the middle than in the tails. Normal distributions are sometimes described as bell shaped.
The Mean of the distribution acts as the location parameter. The standard deviation (which equals the square root of the ) acts as the scale parameter. The normal distribution does not have a shape parameter.
Constructors
Normal | Constructs a new NormalDistribution with mean equal to zero and standard deviation equal to 1. |
Normal | Constructs a new NormalDistribution with specified mean and standard deviation equal to 1. |
Normal | Estimates the parameters of the distribution of a variable assuming it follows a normal distribution. |
Normal | Constructs a new NormalDistribution with specified mean and standard deviation. |
Normal | Estimates the parameters of the distribution of a variable assuming it follows a normal distribution. |
Properties
Entropy |
Gets the entropy of the distribution.
(Overrides Distribution.Entropy) |
Inter |
Returns the inter-quartile range of this distribution.
(Inherited from ContinuousDistribution) |
IsSymmetrical |
Gets whether the distribution is known to be symmetrical around the mean.
(Overrides ContinuousDistribution.IsSymmetrical) |
IsUnimodal |
Gets whether the distribution has one or more modes.
(Inherited from ContinuousDistribution) |
Kurtosis |
Gets the kurtosis of the distribution.
(Overrides Distribution.Kurtosis) |
Mean |
Gets the mean or expectation value of the distribution.
(Overrides Distribution.Mean) |
Median |
Gets the median of the distribution.
(Overrides ContinuousDistribution.Median) |
Mode |
Gets the mode of the distribution.
(Overrides ContinuousDistribution.Mode) |
Number |
Gets the number of modes of the distribution.
(Inherited from ContinuousDistribution) |
Skewness |
Gets the skewness of the distribution.
(Overrides Distribution.Skewness) |
Standard |
Gets the standard deviation of the distribution.
(Overrides Distribution.StandardDeviation) |
Statistic |
Gets the common symbol to describe a statistic
from the distribution.
(Overrides Distribution.StatisticSymbol) |
Support |
Gets the support of the distribution.
(Inherited from ContinuousDistribution) |
Variance |
Gets the variance of the distribution.
(Overrides Distribution.Variance) |
Methods
Cdf |
Evaluates the cumulative distribution function
(CDF) of this distribution for the specified value.
(Inherited from ContinuousDistribution) |
Distribution |
Evaluates the cumulative distribution function
(CDF) of this distribution for the specified value.
(Overrides ContinuousDistribution.DistributionFunction(Double)) |
Distribution | Evaluates the cumulative distribution function (CDF) of this distribution for the specified value. |
Equals | Determines whether the specified object is equal to the current object. (Inherited from Object) |
Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object) |
Get |
Returns an array that contains all the modes of the distribution.
(Inherited from ContinuousDistribution) |
Get | Returns a confidence interval at the specified level. |
Get |
Returns the expectation value of a function.
(Inherited from ContinuousDistribution) |
Get |
Returns the un-normalized expectation value of a function over the specified interval.
(Inherited from ContinuousDistribution) |
Get |
Gets a vector containing a histogram of the expected number of samples
for a given total number of samples.
(Inherited from ContinuousDistribution) |
Get |
Gets a vector containing a histogram of the expected number of samples
for a given total number of samples.
(Inherited from ContinuousDistribution) |
Get |
Gets a vector whose bins contain the expected number of samples
for a given total number of samples.
(Inherited from ContinuousDistribution) |
GetHashCode | Serves as the default hash function. (Inherited from Object) |
Get |
Returns a sequence of random samples from the distribution.
(Inherited from ContinuousDistribution) |
Get |
Returns a sequence of random samples from the distribution.
(Inherited from ContinuousDistribution) |
Get |
Returns a sequence of random samples of the specified length from the distribution.
(Inherited from ContinuousDistribution) |
GetType | Gets the Type of the current instance. (Inherited from Object) |
Hazard |
Returns the probability of failure at the specified value.
(Inherited from ContinuousDistribution) |
Inverse |
Returns the inverse of the DistributionFunction(Double).
(Inherited from ContinuousDistribution) |
Inverse |
Returns the sample value at the specified percentile.
(Overrides ContinuousDistribution.InverseDistributionFunction(Double)) |
Inverse | Returns the inverse of the DistributionFunction(Double). |
Left |
Returns the probability that a sample from the distribution
is less than the specified value.
(Inherited from ContinuousDistribution) |
Log |
Returns the logarithm of the probability density function
(PDF) of this distribution for the specified value.
(Overrides ContinuousDistribution.LogProbabilityDensityFunction(Double)) |
MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object) |
Moment |
Returns the value of the moment function of the specified order.
(Overrides ContinuousDistribution.MomentFunction(Int32, Double)) |
Returns the value of the probability density function
(PDF) of this distribution for the specified value.
(Inherited from ContinuousDistribution) | |
Probability |
Returns the probability that a sample taken from the
distribution lies inside the specified interval.
(Inherited from ContinuousDistribution) |
Probability |
Returns the value of the probability density function
(PDF) of this distribution for the specified value.
(Overrides ContinuousDistribution.ProbabilityDensityFunction(Double)) |
Right |
Returns the probability that a sample from the distribution
is larger than the specified value.
(Inherited from ContinuousDistribution) |
Sample() |
Returns a random sample from the distribution.
(Inherited from ContinuousDistribution) |
Sample( |
Returns a vector of random samples from the distribution.
(Inherited from ContinuousDistribution) |
Sample( |
Returns a random sample from the distribution.
(Overrides ContinuousDistribution.Sample(Random)) |
Sample( |
Returns a vector of random samples from the distribution.
(Inherited from ContinuousDistribution) |
Sample( | Returns a single random sample from a normal distribution with specified mean and standard deviation equal to 1. |
Sample( | Returns a single random sample from a normal distribution with the specified parameters. |
Sample |
Fills a list with random numbers from the distribution.
(Inherited from ContinuousDistribution) |
Sample |
Fills part of a list with random numbers from the distribution.
(Overrides ContinuousDistribution.SampleInto(Random, IList<Double>, Int32, Int32)) |
Survivor |
Evaluates the survivor distribution function
(SDF) of this distribution for the specified value.
(Inherited from ContinuousDistribution) |
ToString | Returns a string that represents the current object. (Overrides Object.ToString()) |
Two |
Returns the probability that a sample from the distribution deviates from the mean more than
the specified value.
(Inherited from ContinuousDistribution) |
ZScore | Returns the z-score of a sample. |
Fields
Standard | Represents the standard NormalDistribution. |