> ## 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.

# Hill Estimator for Tail Index

> Estimates the tail index (shape parameter) using the Hill estimator, a simple non-parametric method for heavy-tailed distributions. The tail index determines how fat the tails are - higher values indicate heavier tails and more extreme events. Used for quick tail risk assessment and for calibrating more sophisticated models. [Tier: PRO, Credits: 5]



## OpenAPI

````yaml api-specs/risk.json post /quantlib/risk/evt/hill
openapi: 3.1.0
info:
  title: FinceptQuantLib API - Risk Module
  description: >-
    Professional-grade risk management endpoints including Value at Risk (VaR),
    stress testing, copulas, extreme value theory (EVT), XVA calculations,
    sensitivities, and portfolio hedging. Part of the Pro Tier (5 credits per
    request).
  version: 3.0.0
  contact:
    name: Fincept API Support
    url: https://fincept.in
    email: support@fincept.in
servers:
  - url: https://api.fincept.in
    description: Fincept API Production Server
security:
  - APIKeyHeader: []
tags:
  - name: quantlib-risk
    description: Risk Management Module - Pro Tier (5 credits/request)
    x-displayName: Risk
paths:
  /quantlib/risk/evt/hill:
    post:
      tags:
        - quantlib-risk
      summary: Hill Estimator for Tail Index
      description: >-
        Estimates the tail index (shape parameter) using the Hill estimator, a
        simple non-parametric method for heavy-tailed distributions. The tail
        index determines how fat the tails are - higher values indicate heavier
        tails and more extreme events. Used for quick tail risk assessment and
        for calibrating more sophisticated models. [Tier: PRO, Credits: 5]
      operationId: hill_estimator
      requestBody:
        required: true
        content:
          application/json:
            schema:
              type: object
              required:
                - data
              properties:
                data:
                  type: array
                  description: Loss or return data for tail analysis
                  items:
                    type: number
                  minItems: 100
                  example:
                    - -0.02
                    - -0.06
                    - -0.04
                    - -0.09
            example:
              data:
                - -0.02
                - -0.06
                - -0.04
                - -0.09
                - -0.03
                - -0.11
                - -0.05
                - -0.08
      responses:
        '200':
          description: Hill estimator results
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      xi:
                        type: number
                        description: Tail index estimate (shape parameter)
                        example: 0.28
                      standard_error:
                        type: number
                        description: Standard error of the estimate
                        example: 0.045
              example:
                success: true
                data:
                  xi: 0.28
                  standard_error: 0.045
        '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 for this request
      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

````