Comparative Study of Data Generation for Normal, Lognormal, and Gamma Distributions using PLS and Usury Models

Abstract

Mathematical modeling in the world of economics and banking has particular relevance, especially in terms of providing capital for business activities, particularly for Micro, Small, and Medium Enterprises (MSMEs). Currently, banking activities are predominantly dominated by conventional banks that apply interest, which in Islamic Sharia is considered as riba, and it is incumbent upon Muslims to avoid riba and conduct all their affairs in accordance with Islamic Sharia. This research discusses a mathematical model of a profit-loss sharing system in accordance with Islamic Sharia using the profit-loss sharing model scheme, which is one of the investment models in Islamic finance with a musyarakah contract. The data is derived from the daily profit and loss of a micro trader for the period of September 2023 in Cijantung, East Jakarta, which is then generated for periods of 35, 40, and 50 days, following normal, lognormal, and gamma distributions, with an investment capital of Rp 1,500,000, Rp 3,000,000, and Rp 4,500,000, and profit-sharing portions of 2%, 5%, and 7%. This research is capable of demonstrating a profit-sharing scheme and optimization functions in profit distribution, as well as determining parameters that are more advantageous for traders and capital owners compared to the usury model because the imposed penalties are considered burdensome for the public. Generating data following a normal distribution provides a more realistic profit-sharing scheme but a lognormal and gamma distribution yields the largest profit-sharing portion for investor and trader.