curl --request POST \
  --url https://api.fincept.in/quantlib/physics/entropy/differential \
  --header 'Content-Type: application/json' \
  --header 'X-API-Key: <api-key>' \
  --data '
{
  "distribution": "gaussian",
  "sigma": 0.015
}
'

{
  "success": true,
  "data": {
    "differential_entropy": -2.8327,
    "distribution": "gaussian"
  }
}

{
  "detail": "Invalid API key"
}

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

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

quantlib-physics

Calculate Differential Entropy

Calculates the differential entropy for continuous probability distributions (Gaussian or exponential). Differential entropy extends the concept of entropy to continuous random variables and can be negative (unlike discrete entropy). Essential for continuous financial models, option pricing, and Bayesian inference.

Use Cases:

Measure uncertainty in continuous return distributions
Information content in continuous signals
Gaussian process modeling
Entropy of volatility distributions
Continuous-time information theory

Formulas:

Gaussian: h(X) = 0.5 log(2πe σ²)
Exponential: h(X) = 1 + log(λ⁻¹)

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

POST

quantlib

physics

entropy

differential

curl --request POST \
  --url https://api.fincept.in/quantlib/physics/entropy/differential \
  --header 'Content-Type: application/json' \
  --header 'X-API-Key: <api-key>' \
  --data '
{
  "distribution": "gaussian",
  "sigma": 0.015
}
'

{
  "success": true,
  "data": {
    "differential_entropy": -2.8327,
    "distribution": "gaussian"
  }
}

{
  "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

distribution

enum<string>

default:gaussian

Type of continuous distribution

Available options:

gaussian,

exponential

Example:

"gaussian"

sigma

number

default:1

Standard deviation (for Gaussian distribution)

Example:

0.2

rate

number

default:1

Rate parameter λ (for exponential distribution)

Example:

0.5

Response

Differential 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 Differential Entropy

Authorizations

Body

Response