define_distribution
Define a probability distribution with PDF/PMF for modeling uncertainty, variability, error propagation, or Monte Carlo simulations. Supports continuous and discrete types.
Instructions
Define a probability distribution.
═══════════════════════════════════════════════════════════════════════
🆕 NOT AVAILABLE IN SYMPY-MCP! Uses sympy.stats module.
═══════════════════════════════════════════════════════════════════════
Use cases:
- Model measurement uncertainty
- Population variability in pharmacokinetics
- Error propagation
- Monte Carlo preparation
Supported distributions:
- Continuous: normal, exponential, uniform, gamma, beta, lognormal
- Discrete: poisson, binomial, geometric
Args:
distribution_type: Type of distribution
parameters: Distribution parameters (as strings for symbolic)
name: Name of the random variable
Returns:
Distribution definition with PDF/PMF
Examples:
# Normal distribution
define_distribution("normal", {"mean": "mu", "std": "sigma"}, "X")
# Exponential (for waiting times)
define_distribution("exponential", {"rate": "lambda"}, "T")
# Log-normal (for PK parameters)
define_distribution("lognormal", {"mean": "mu", "std": "sigma"}, "CL")
Input Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| name | No | X | |
| parameters | Yes | ||
| distribution_type | Yes |
Output Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
No arguments | |||