Create a new budget with a name, average daily limit, weight function, and relevant discount IDs. The budget_id is generated by the system after creation.

Weight Function Explanation:
The weight function determines how discounts are applied to the budget when a discount is triggered. It is defined as a mathematical expression, with a default value of w * x, where:

• w: Represents the discount-specific weight, which adjusts the impact of the discount based on its priority.
• x: Represents a random draw from a beta distribution, introducing variability that captures uncertainty.

The product of these factors (w multiplied by x) determines the effective discount applied to the budget, allowing for dynamic adjustments that balance fixed priorities with stochastic variation.