curl --request POST \
  --url https://api.fincept.in/quantlib/physics/entropy/renyi \
  --header 'Content-Type: application/json' \
  --header 'X-API-Key: <api-key>' \
  --data '
{
  "probabilities": [
    0.5,
    0.3,
    0.15,
    0.05
  ],
  "alpha": 2,
  "base": 2.718281828459045
}
'

{
  "success": true,
  "data": {
    "renyi_entropy": 0.9562,
    "alpha": 2
  }
}

{
  "detail": "Invalid API key"
}

{
  "detail": "Insufficient credits. This endpoint requires 5 credits."
}

{
  "detail": [
    {
      "loc": [
        "<string>"
      ],
      "msg": "<string>",
      "type": "<string>"
    }
  ]
}

quantlib-physics

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]

POST

quantlib

physics

entropy

renyi

curl --request POST \
  --url https://api.fincept.in/quantlib/physics/entropy/renyi \
  --header 'Content-Type: application/json' \
  --header 'X-API-Key: <api-key>' \
  --data '
{
  "probabilities": [
    0.5,
    0.3,
    0.15,
    0.05
  ],
  "alpha": 2,
  "base": 2.718281828459045
}
'

{
  "success": true,
  "data": {
    "renyi_entropy": 0.9562,
    "alpha": 2
  }
}

{
  "detail": "Invalid API key"
}

{
  "detail": "Insufficient credits. This endpoint requires 5 credits."
}

{
  "detail": [
    {
      "loc": [
        "<string>"
      ],
      "msg": "<string>",
      "type": "<string>"
    }
  ]
}

Authorizations

X-API-Key

string

header

required

API key for authentication. Get your key at https://api.fincept.in/auth/register

Body

application/json

probabilities

number[]

required

Discrete probability distribution (must sum to 1)

Example:

[0.5, 0.3, 0.15, 0.05]

alpha

number

required

Renyi parameter (α=0: max-entropy, α=1: Shannon, α=2: collision entropy, α→∞: min-entropy)

Example:

2

base

number

default:2.718281828459045

Logarithm base for entropy calculation

Example:

2.718281828459045

Response

Renyi entropy calculated successfully

success

boolean

Example:

true

data

object

Show child attributes

Free Tier (0 credits)

Basic Tier (1 credit)

Standard Tier (2 credits)

Pro Tier (5 credits)

Enterprise Tier (10 credits)

Calculate Renyi Entropy

Authorizations

Body

Response