> ## Documentation Index
> Fetch the complete documentation index at: https://docs.fincept.in/llms.txt
> Use this file to discover all available pages before exploring further.

# Calculate Renyi Entropy

> Calculates the Renyi entropy, a generalization of Shannon entropy parameterized by α. Different α values emphasize different aspects of the distribution: α→0 emphasizes rare events, α=1 recovers Shannon entropy, α→∞ emphasizes the most probable event. Useful for risk-sensitive information measures in finance.

**Use Cases:**
- Risk-sensitive portfolio uncertainty measures
- Tail risk assessment (low α emphasizes tails)
- Robust entropy estimation for noisy data
- Multi-scale information analysis
- Compare distributions with varying risk preferences

**Formula:** H_α(X) = (1/(1-α)) log(Σ p(x)^α)

**Credits:** 5 credits per request (Pro Tier) [Tier: ENTERPRISE, Credits: 10]



## OpenAPI

````yaml api-specs/physics.json post /quantlib/physics/entropy/renyi
openapi: 3.1.0
info:
  title: FinceptQuantLib API - Physics Module
  description: >-
    Physics and Information Theory module for FinceptQuantLib API. Includes
    Shannon/Renyi/Tsallis entropy, KL/JS divergence, mutual information,
    transfer entropy, Fisher information, Boltzmann distribution, Ising model,
    maximum entropy, thermodynamics (free energy, Carnot cycle, van der Waals
    equation), and Maxwell relations. **Pro Tier required. 5 credits per
    request.**
  version: 3.0.0
  contact:
    name: Fincept API Support
    url: https://fincept.in
servers:
  - url: https://api.fincept.in
    description: Fincept API Production Server
security:
  - APIKeyHeader: []
tags:
  - name: quantlib-physics
    description: Physics and Information Theory module for FinceptQuantLib API
    x-displayName: Physics
paths:
  /quantlib/physics/entropy/renyi:
    post:
      tags:
        - quantlib-physics
      summary: Calculate Renyi Entropy
      description: >-
        Calculates the Renyi entropy, a generalization of Shannon entropy
        parameterized by α. Different α values emphasize different aspects of
        the distribution: α→0 emphasizes rare events, α=1 recovers Shannon
        entropy, α→∞ emphasizes the most probable event. Useful for
        risk-sensitive information measures in finance.


        **Use Cases:**

        - Risk-sensitive portfolio uncertainty measures

        - Tail risk assessment (low α emphasizes tails)

        - Robust entropy estimation for noisy data

        - Multi-scale information analysis

        - Compare distributions with varying risk preferences


        **Formula:** H_α(X) = (1/(1-α)) log(Σ p(x)^α)


        **Credits:** 5 credits per request (Pro Tier) [Tier: ENTERPRISE,
        Credits: 10]
      operationId: renyi_entropy
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - probabilities
                - alpha
              properties:
                probabilities:
                  type: array
                  items:
                    type: number
                  description: Discrete probability distribution (must sum to 1)
                  example:
                    - 0.5
                    - 0.3
                    - 0.15
                    - 0.05
                alpha:
                  type: number
                  description: >-
                    Renyi parameter (α=0: max-entropy, α=1: Shannon, α=2:
                    collision entropy, α→∞: min-entropy)
                  example: 2
                base:
                  type: number
                  description: Logarithm base for entropy calculation
                  default: 2.718281828459045
                  example: 2.718281828459045
            examples:
              collision_entropy:
                summary: Collision entropy (α=2)
                value:
                  probabilities:
                    - 0.5
                    - 0.3
                    - 0.15
                    - 0.05
                  alpha: 2
                  base: 2.718281828459045
              min_entropy:
                summary: Min-entropy (α→∞, use large value)
                value:
                  probabilities:
                    - 0.6
                    - 0.25
                    - 0.1
                    - 0.05
                  alpha: 100
                  base: 2
      responses:
        '200':
          description: Renyi entropy calculated successfully
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      renyi_entropy:
                        type: number
                        description: Renyi entropy value
                        example: 0.9562
                      alpha:
                        type: number
                        description: Renyi parameter used
                        example: 2
        '401':
          $ref: '#/components/responses/UnauthorizedError'
        '402':
          $ref: '#/components/responses/InsufficientCreditsError'
        '422':
          $ref: '#/components/responses/ValidationError'
components:
  responses:
    UnauthorizedError:
      description: Authentication information is missing or invalid
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Invalid API key
    InsufficientCreditsError:
      description: Insufficient API credits
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Insufficient credits. This endpoint requires 5 credits.
    ValidationError:
      description: Request validation error
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: array
                items:
                  type: object
                  properties:
                    loc:
                      type: array
                      items:
                        type: string
                    msg:
                      type: string
                    type:
                      type: string
  securitySchemes:
    APIKeyHeader:
      type: apiKey
      in: header
      name: X-API-Key
      description: >-
        API key for authentication. Get your key at
        https://api.fincept.in/auth/register

````