Class DistributionFitResult<T>

Namespace

AiDotNet.Models.Results

Assembly

AiDotNet.dll

Represents the result of fitting a statistical distribution to a dataset, including the distribution type, goodness of fit measure, and estimated parameters.

public class DistributionFitResult<T>

Type Parameters

T

The numeric type used for statistical values, typically float or double.

Inheritance

object

DistributionFitResult<T>

Inherited Members

object.Equals(object)

object.Equals(object, object)

object.GetHashCode()

object.GetType()

object.MemberwiseClone()

object.ReferenceEquals(object, object)

object.ToString()

Remarks

When analyzing data, it's often useful to determine which statistical distribution best describes the data. This class stores the results of such distribution fitting, including the type of distribution that best fits the data, a measure of how well the distribution fits (goodness of fit), and the estimated parameters of the distribution. The goodness of fit measure allows for comparing different distribution types to determine which one provides the best representation of the data. The class uses generic type parameter T to support different numeric types for the statistical values, such as float, double, or decimal.

For Beginners: This class stores information about how well a statistical distribution matches your data.

When analyzing data, you often want to know:

• Which standard statistical distribution (like Normal, Exponential, etc.) best describes your data
• How well that distribution fits your data
• What the specific parameters of that distribution are

This class stores all that information after a distribution fitting process, making it easy to:

• Identify the best distribution for your data
• Compare how well different distributions fit
• Access the parameters needed to use the distribution for further analysis

For example, if your data follows a normal distribution, this class would tell you that, provide a measure of how well it fits, and give you the mean and standard deviation parameters.

Constructors

DistributionFitResult(INumericOperations<T>?)

Initializes a new instance of the DistributionFitResult class with default values.

public DistributionFitResult(INumericOperations<T>? ops = null)

Parameters

ops INumericOperations<T>

Optional numeric operations provider for type T. If null, default operations will be used.

Remarks

This constructor creates a new DistributionFitResult instance and initializes the GoodnessOfFit property to zero and the Parameters property to an empty dictionary. It takes an optional INumericOperations<T> parameter that provides numeric operations for the generic type T. If this parameter is null, the constructor uses MathHelper.GetNumericOperations<T>() to obtain the default numeric operations for type T. This allows the class to work with different numeric types such as float, double, or decimal. The constructor provides a clean starting point for storing distribution fitting results.

For Beginners: This constructor creates a new result object with default values.

When a new DistributionFitResult is created:

• The goodness of fit is initialized to zero
• The parameters dictionary is created as empty
• Numeric operations appropriate for type T are set up

The ops parameter:

• Provides mathematical operations for the numeric type T
• Can be null, in which case default operations are used
• Allows the class to work with different numeric types (float, double, etc.)

This initialization is important because:

• It ensures consistent behavior regardless of how the object is created
• It prevents potential issues with uninitialized values
• It makes the code more robust across different numeric types

You typically won't need to call this constructor directly, as it will be used internally by the distribution fitting process.

Properties

DistributionType

Gets or sets the type of distribution that best fits the data.

public DistributionType DistributionType { get; set; }

Property Value

DistributionType

A value from the DistributionType enumeration indicating the distribution type.

Remarks

This property specifies the type of statistical distribution that was fitted to the data. Common distribution types include Normal (Gaussian), Exponential, Weibull, Gamma, Beta, and others. Each distribution type has different characteristics and is suitable for modeling different kinds of data. For example, the Normal distribution is often used for data that clusters around a mean value, while the Exponential distribution is suitable for modeling time between events in a Poisson process. The distribution type is typically determined by comparing the goodness of fit measures for different distributions and selecting the one with the best fit.

For Beginners: This property tells you which statistical distribution best matches your data.

The distribution type:

• Identifies which standard probability distribution was found to fit your data
• Each distribution has different characteristics and is suitable for different types of data

Common distribution types include:

• Normal (Gaussian): The classic bell curve, good for many natural phenomena
• Exponential: Good for modeling time between random events
• Uniform: Equal probability across a range
• Poisson: Good for counting rare events in fixed time/space
• Weibull: Often used for reliability and lifetime data

Knowing the distribution type helps you:

• Understand the underlying patterns in your data
• Make predictions about future observations
• Apply appropriate statistical methods for further analysis

For example, if this property is set to DistributionType.Normal, it means your data approximately follows a bell curve pattern.

GoodnessOfFit

Gets or sets the goodness of fit measure. Lower values indicate better fit.

public T GoodnessOfFit { get; set; }

Property Value

T

A numeric value representing the goodness of fit, initialized to zero.

Remarks

This property represents a measure of how well the selected distribution fits the data. Common goodness of fit measures include the Kolmogorov-Smirnov statistic, Anderson-Darling statistic, or negative log-likelihood. Lower values typically indicate a better fit, meaning the distribution more closely matches the observed data. This measure can be used to compare different distribution types to determine which one provides the best representation of the data. The specific interpretation of the goodness of fit value depends on the measure used, but it generally allows for relative comparisons between different distribution fits.

For Beginners: This value tells you how well the distribution matches your data.

The goodness of fit measure:

• Quantifies how closely the distribution matches your actual data
• Lower values indicate a better fit (less discrepancy between the model and data)
• Allows you to compare different distributions to find the best one

This value is important because:

• It helps you determine if the distribution is a good model for your data
• It allows you to compare multiple distribution types objectively
• It can indicate when no standard distribution fits your data well

Common goodness of fit measures include:

• Kolmogorov-Smirnov statistic: Based on the maximum difference between empirical and theoretical CDFs
• Anderson-Darling statistic: Similar but gives more weight to the tails of the distribution
• Negative log-likelihood: Based on the probability of observing your data given the distribution

For example, if you fit both Normal and Exponential distributions to your data, the one with the lower goodness of fit value would be considered the better match.

Parameters

Gets or sets the parameters of the fitted distribution. The keys are parameter names, and the values are the corresponding parameter values.

public Dictionary<string, T> Parameters { get; set; }

Property Value

Dictionary<string, T>

A dictionary mapping parameter names to their values, initialized as an empty dictionary.

Remarks

This property stores the estimated parameters of the fitted distribution as a dictionary, where the keys are the parameter names and the values are the corresponding parameter values. The specific parameters depend on the distribution type. For example, a Normal distribution has "mean" and "standardDeviation" parameters, an Exponential distribution has a "rate" parameter, and a Weibull distribution has "shape" and "scale" parameters. These parameters fully define the distribution and can be used for further statistical analysis, such as calculating probabilities, generating random samples, or making predictions. The parameter values are estimated from the data during the distribution fitting process, typically using methods such as maximum likelihood estimation or method of moments.

For Beginners: This dictionary contains the specific values that define the distribution.

The distribution parameters:

• Are the specific values that define the shape and characteristics of the distribution
• Vary depending on which distribution type was selected
• Are estimated from your data during the fitting process

Common parameters for different distributions:

• Normal distribution: "mean" and "standardDeviation"
• Exponential distribution: "rate" or "lambda"
• Uniform distribution: "minimum" and "maximum"
• Weibull distribution: "shape" and "scale"

These parameters are important because:

• They completely define the distribution
• They allow you to calculate probabilities and statistics
• They can be used to generate random samples from the distribution
• They often have meaningful interpretations in your domain

For example, if fitting a Normal distribution to height data, the "mean" parameter would represent the average height, and "standardDeviation" would represent how spread out the heights are around that average.