Struct ShapeMetrics 

pub struct ShapeMetrics {
    pub skewness: Decimal,
    pub kurtosis: Decimal,
    pub peaks: Vec<Point2D>,
    pub valleys: Vec<Point2D>,
    pub inflection_points: Vec<Point2D>,
}

Represents shape-related analysis metrics for a given curve.

Overview

The ShapeMetrics structure encapsulates shape-related properties and critical points describing a curve’s geometrical behavior. It’s primarily used for mathematical and statistical analysis of curves representing data distributions or mathematical functions.

Fields

• skewness - A measure of distribution asymmetry. Positive values indicate right tailing while negative values indicate left tailing.

• kurtosis - A measure of the “tailedness” or presence of outliers in the distribution. Higher values indicate heavier tails and more outliers compared to a normal distribution.

• peaks - Collection of points representing local or global maxima along the curve, stored as Point2D coordinates.

• valleys - Collection of points representing local or global minima along the curve, stored as Point2D coordinates.

• inflection_points - Points where the curve changes concavity (transitioning from concave up to concave down or vice versa), stored as Point2D coordinates.

Applications

This structure is commonly used in:

• Financial analysis to identify trend reversals or extreme price levels
• Statistical distribution analysis to characterize data shape properties
• Mathematical modeling to identify critical points in curve functions
• Visualization and interpretation of complex curve behaviors

Relationship with Other Structures

ShapeMetrics is typically part of the larger AnalysisResult structure that provides comprehensive curve analysis. It uses Point2D to represent all positional data with high-precision Decimal values.

Fields

skewness: Decimal

Describes the asymmetry of the curve’s distribution. A positive value indicates a right tail (right-skewed distribution), while a negative value indicates a left tail (left-skewed distribution). A value close to zero suggests symmetry.

kurtosis: Decimal

Indicates the “tailedness” or presence of outliers in the curve’s distribution. Higher values correspond to heavier tails and more outliers compared to a normal distribution. Standard normal distribution has kurtosis of 3.0. Often expressed as excess kurtosis (kurtosis - 3).

peaks: Vec<Point2D>

Collection of Point2D instances representing local or global maxima (peaks) along the curve. These points have higher y-values than their immediate neighboring points.

valleys: Vec<Point2D>

Collection of Point2D instances representing local or global minima (valleys) along the curve. These points have lower y-values than their immediate neighboring points.

inflection_points: Vec<Point2D>

Points where the curve changes concavity, transitioning from concave up to concave down (or vice versa). At these points, the second derivative equals zero while changing sign.

Trait Implementations

impl Clone for ShapeMetrics

fn clone(&self) -> Self

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl ComposeSchema for ShapeMetrics

fn compose(generics: Vec<RefOr<Schema>>) -> RefOr<Schema>

impl Debug for ShapeMetrics

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Display for ShapeMetrics

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Serialize for ShapeMetrics

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl ToSchema for ShapeMetrics

fn name() -> Cow<'static, str>

Return name of the schema.

fn schemas(schemas: &mut Vec<(String, RefOr<Schema>)>)

Implement reference utoipa::openapi::schema::Schemas for this type.