> ## 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 Maximum Entropy Distribution

> Computes the maximum entropy probability distribution subject to given moment constraints. The maximum entropy principle selects the least informative distribution consistent with constraints, avoiding unwarranted assumptions. Widely used in portfolio optimization, risk-neutral pricing, and statistical inference.

**Use Cases:**
- Portfolio optimization with return/variance constraints
- Risk-neutral density estimation from option prices
- Bayesian prior selection with limited information
- Robust probability modeling
- Market-implied distribution inference

**Formula:** Maximize H(P) = -Σ p_i log(p_i) subject to Σ f_k(i) p_i = μ_k

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



## OpenAPI

````yaml api-specs/physics.json post /quantlib/physics/max-entropy
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/max-entropy:
    post:
      tags:
        - quantlib-physics
      summary: Calculate Maximum Entropy Distribution
      description: >-
        Computes the maximum entropy probability distribution subject to given
        moment constraints. The maximum entropy principle selects the least
        informative distribution consistent with constraints, avoiding
        unwarranted assumptions. Widely used in portfolio optimization,
        risk-neutral pricing, and statistical inference.


        **Use Cases:**

        - Portfolio optimization with return/variance constraints

        - Risk-neutral density estimation from option prices

        - Bayesian prior selection with limited information

        - Robust probability modeling

        - Market-implied distribution inference


        **Formula:** Maximize H(P) = -Σ p_i log(p_i) subject to Σ f_k(i) p_i =
        μ_k


        **Credits:** 5 credits per request (Pro Tier) [Tier: ENTERPRISE,
        Credits: 10]
      operationId: max_entropy_dist
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - n_states
                - constraint_values
              properties:
                n_states:
                  type: integer
                  description: Number of states in the distribution
                  example: 5
                constraint_values:
                  type: array
                  items:
                    type: number
                  description: >-
                    Target probabilities for each state (constraints). Each
                    value represents the desired probability for the
                    corresponding state index.
                  example:
                    - 0.1
                    - 0.2
                    - 0.3
                    - 0.25
                    - 0.15
            examples:
              mean_constraint:
                summary: Distribution with specific state probabilities
                value:
                  n_states: 5
                  constraint_values:
                    - 0.15
                    - 0.2
                    - 0.3
                    - 0.2
                    - 0.15
              portfolio_optimization:
                summary: Portfolio state constraints
                value:
                  n_states: 4
                  constraint_values:
                    - 0.4
                    - 0.3
                    - 0.2
                    - 0.1
      responses:
        '200':
          description: Maximum entropy distribution computed successfully
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      distribution:
                        type: array
                        items:
                          type: number
                        description: Maximum entropy probability distribution
                        example:
                          - 0.15
                          - 0.2
                          - 0.3
                          - 0.2
                          - 0.15
                      n_states:
                        type: integer
                        description: Number of states
                        example: 5
        '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

````