Student |
Continuous Univariate Student's T-distribution.
Implements the univariate Student t-distribution. For details about this
distribution, see
Wikipedia - Student's t-distribution.
Inheritance HierarchyNamespace: Altaxo.Calc.Distributions
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
SyntaxC#
public class StudentT : IContinuousDistribution, IUnivariateDistribution, IDistribution
The StudentT type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | StudentT | Initializes a new instance of the StudentT class. This is a Student t-distribution with location 0.0 scale 1.0 and degrees of freedom 1. |
| StudentT(Double, Double, Double) | Initializes a new instance of the StudentT class with a particular location, scale and degrees of freedom. |
| StudentT(Double, Double, Double, Random) | Initializes a new instance of the StudentT class with a particular location, scale and degrees of freedom. |
Properties| Name | Description | |
|---|---|---|
 | DegreesOfFreedom | Gets the degrees of freedom (ν) of the Student t-distribution. Range: ν > 0. |
| Entropy | Gets the entropy of the Student t-distribution. |
| Location | Gets the location (μ) of the Student t-distribution. |
| Maximum | Gets the maximum of the Student t-distribution. |
| Mean | Gets the mean of the Student t-distribution. |
| Median | Gets the median of the Student t-distribution. |
| Minimum | Gets the minimum of the Student t-distribution. |
| Mode | Gets the mode of the Student t-distribution. |
| RandomSource | Gets or sets the random number generator which is used to draw random samples. |
| Scale | Gets the scale (σ) of the Student t-distribution. Range: σ > 0. |
| Skewness | Gets the skewness of the Student t-distribution. |
| StdDev | Gets the standard deviation of the Student t-distribution. |
| Variance | Gets the variance of the Student t-distribution. |
Methods| Name | Description | |
|---|---|---|
 | CDF | Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x). |
| CumulativeDistribution | Computes the cumulative distribution (CDF) of the distribution at x, i.e. P(X ≤ x). |
| Density | Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x. |
| DensityLn | Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x). |
| 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) |
| GetHashCode | Serves as the default hash function. (Inherited from Object) |
| GetType | Gets the Type of the current instance. (Inherited from Object) |
| InvCDF | Computes the inverse of the cumulative distribution function (InvCDF) for the distribution at the given probability. This is also known as the quantile or percent point function. |
| InverseCumulativeDistribution | Computes the inverse of the cumulative distribution function (InvCDF) for the distribution at the given probability. This is also known as the quantile or percent point function. |
| IsValidParameterSet | Tests whether the provided values are valid parameters for this distribution. |
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object) |
| Computes the probability density of the distribution (PDF) at x, i.e. ∂P(X ≤ x)/∂x. | |
| PDFLn | Computes the log probability density of the distribution (lnPDF) at x, i.e. ln(∂P(X ≤ x)/∂x). |
| Sample | Generates a sample from the Student t-distribution. |
| Sample(Double, Double, Double) | Generates a sample from the Student t-distribution. |
| Sample(Random, Double, Double, Double) | Generates a sample from the Student t-distribution. |
| Samples | Generates a sequence of samples from the Student t-distribution. |
| Samples(Double) | Fills an array with samples generated from the distribution. |
| Samples(Double, Double, Double) | Generates a sequence of samples from the Student t-distribution using the Box-Muller algorithm. |
| Samples(Double, Double, Double, Double) | Fills an array with samples generated from the distribution. |
| Samples(Random, Double, Double, Double) | Generates a sequence of samples from the Student t-distribution using the Box-Muller algorithm. |
| Samples(Random, Double, Double, Double, Double) | Fills an array with samples generated from the distribution. |
| ToString |
A string representation of the distribution.
(Overrides ObjectToString) |
RemarksWe use a slightly generalized version (compared to Wikipedia) of the Student t-distribution. Namely, one which also parameterizes the location and scale. See the book "Bayesian Data Analysis" by Gelman et al. for more details.
The density of the Student t-distribution p(x|mu,scale,dof) = Gamma((dof+1)/2) (1 + (x - mu)^2 / (scale * scale * dof))^(-(dof+1)/2) / (Gamma(dof/2)*Sqrt(dof*pi*scale)).
The distribution will use the Random by default. Users can get/set the random number generator by using the RandomSource property.
The statistics classes will check all the incoming parameters whether they are in the allowed range. This might involve heavy computation. Optionally, by setting Control.CheckDistributionParameters to false, all parameter checks can be turned off.
See Also