The process of building a swimming pool is not just a simple dig-an-empty-space-and-fill-it-with-water procedure. It's a project that entails precise planning and budgeting, from the inception of the idea to the finishing touches on the tile work. In order to navigate this potentially daunting task, it's crucial to devise a clear and detailed budget. Here, we will elucidate the process of creating a budget for your pool construction project using various economic, statistical and mathematical principles.

To begin with, it's essential to comprehend the main categories of costs associated with pool construction: design, excavation, materials, labor, and maintenance. Each of these domains is subject to the principles of cost accounting, which will help us itemize and manage these costs effectively.

The design phase comprises the expenses of drafting a blueprint for your pool – this includes the cost of a professional architect or a landscape designer. It encompasses the conceptualization of the pool's size, shape, depth, and the integration of the pool design into the broader landscape design. This cost is subject to the principles of supply and demand economics. In areas where there are numerous pool designers and high competition, prices may be lower due to market saturation.

The second cost domain, excavation, involves the expense of digging and preparing the site for pool construction. This is dependent on the topography of the land, the soil type, and accessibility of the site. For instance, rocky soils might necessitate more labor-intense processes or specialized machinery, increasing the overall cost. This can be accurately predicted using the field of geotechnical engineering.

The materials category encompasses the cost of concrete, tiles, pool equipment like pumps and heaters, and any additional features such as waterfalls or pool lighting. It's essential to account for the cost of each material required and to factor in the potential price fluctuations. For instance, if we adhere to the Law of One Price (LOOP), an economic theory that suggests that "a good must sell for the same price in all locations", then the price of concrete in your local area should be similar to its price globally, barring transportation and taxes.

Labor costs involve the charges of skilled workers who will bring the pool design to life. This is generally a significant portion of the total pool construction cost. Labor market trends, such as local minimum wages and labor availability, can greatly influence this cost.

Finally, it's crucial to consider the ongoing cost of pool maintenance. This includes regular cleaning, chemical balancing, potential repair work, and utilities like water and electricity. The Pareto Principle, often referred to as the 80/20 rule, can be applied here. This principle posits that 80% of your maintenance time could be taken up by 20% of the tasks. Identifying these tasks in advance can save you time and money in the long run.

While this guide provides a roadmap to establishing a detailed and accurate budget, one must remember that every pool construction project is unique. Unforeseen circumstances might occur, altering the initial budget. It's crucial to have a contingency fund in place. In the realm of project management, employing the PERT (Program Evaluation and Review Technique) can be advantageous. This allows us to estimate the project's timeframe and costs using the best-case scenario (optimistic), most-likely scenario, and worst-case scenario (pessimistic).

In conclusion, creating a budget for your pool construction project requires an intricate understanding of various cost domains and a careful application of multiple principles from economics, mathematics, and statistics. It's a game of numbers, but with the right planning and foresight, it can lead to the creation of a personal oasis that provides endless fun and relaxation.