> ## 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 Fisher Information

> Calculates the Fisher information, which measures the amount of information that an observable random variable carries about an unknown parameter. Fisher information is fundamental in parameter estimation, providing the Cramér-Rao lower bound on estimator variance. Higher Fisher information means more precise parameter estimates are possible.

**Use Cases:**
- Assess quality of parameter estimates in models
- Determine optimal data collection strategies
- Evaluate information content for calibration
- Cramér-Rao bounds for risk measures
- Model sensitivity and parameter identifiability

**Formula:** I(θ) = E[(∂log f(X;θ)/∂θ)²]

Cramér-Rao bound: Var(θ̂) ≥ 1/I(θ)

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



## OpenAPI

````yaml api-specs/physics.json post /quantlib/physics/entropy/fisher-information
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/fisher-information:
    post:
      tags:
        - quantlib-physics
      summary: Calculate Fisher Information
      description: >-
        Calculates the Fisher information, which measures the amount of
        information that an observable random variable carries about an unknown
        parameter. Fisher information is fundamental in parameter estimation,
        providing the Cramér-Rao lower bound on estimator variance. Higher
        Fisher information means more precise parameter estimates are possible.


        **Use Cases:**

        - Assess quality of parameter estimates in models

        - Determine optimal data collection strategies

        - Evaluate information content for calibration

        - Cramér-Rao bounds for risk measures

        - Model sensitivity and parameter identifiability


        **Formula:** I(θ) = E[(∂log f(X;θ)/∂θ)²]


        Cramér-Rao bound: Var(θ̂) ≥ 1/I(θ)


        **Credits:** 5 credits per request (Pro Tier) [Tier: ENTERPRISE,
        Credits: 10]
      operationId: fisher_information
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - data
                - parameter
              properties:
                data:
                  type: array
                  items:
                    type: number
                  description: Sample data for Fisher information estimation
                  example:
                    - 0.95
                    - 1.02
                    - 0.98
                    - 1.05
                    - 0.97
                    - 1.01
                    - 0.99
                    - 1.03
                parameter:
                  type: number
                  description: Parameter value at which to evaluate Fisher information
                  default: 1
                  example: 1
            examples:
              return_samples:
                summary: Estimate Fisher information from returns
                value:
                  data:
                    - 0.012
                    - -0.005
                    - 0.018
                    - 0.003
                    - -0.008
                    - 0.015
                    - 0.007
                    - -0.002
                  parameter: 0.01
              volatility_estimation:
                summary: Information for volatility parameter
                value:
                  data:
                    - 0.15
                    - 0.18
                    - 0.16
                    - 0.2
                    - 0.17
                    - 0.19
                    - 0.16
                    - 0.21
                  parameter: 0.18
      responses:
        '200':
          description: Fisher information calculated successfully
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      fisher_information:
                        type: number
                        description: >-
                          Fisher information I(θ) - higher means more
                          information about parameter
                        example: 125.67
        '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

````