A New Tangent-Generated Probabilistic Approach with Symmetrical and Asymmetrical Natures: Monte Carlo Simulation with Reliability Applications

• Published in: Symmetry (Basel) Vol. 15; no. 11; p. 2066
• Main Authors: Alshanbari, Huda M., Al-Mofleh, Hazem, Seong, Jin-Taek, Khosa, Saima K.
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-11-2023
• Subjects: Decision-making; Distribution (Probability theory); flexible Weibull extension; Goodness of fit; Kurtosis; Mathematical models; Methods; Modelling; Monte Carlo method; Monte Carlo simulation; Parameterization; Parameters; Probabilistic methods; properties; Random variables; Reliability; reliability data; simulation; Skewness; Statistical analysis; Statistical tests; tangent function; waiting time; Weibull distribution
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym15112066

It is proven evidently that probability distributions have a significant role in data modeling for decision-making. Due to the indispensable role of probability distributions for data modeling in applied fields, a series of probability distributions have been introduced and implemented. However, most newly developed probability distributions involve between one and eight additional parameters. Sometimes the additional parameters lead to re-parametrization problems. Therefore, the development of new probability distributions without additional parameters is an interesting research topic. In this paper, we study a new probabilistic method without incorporating any additional parameters. The proposed approach is based on a tangent function and may be called a new tangent-G (NT-G) family of distributions. Certain properties of the NT-G distributions are derived. Based on the NT-G method, a new flexible probability distribution called a new tangent flexible Weibull (NTF-Weibull) distribution is studied. The parameters of the NTF-Weibull distribution are estimated using seven different estimation methods. Based on these eight estimations, a brief simulation of the NTF-Weibull distribution is also provided. Finally, we prove the applicability of the NTF-Weibull distribution by analyzing two waiting-time data sets taken from the reliability sector. We consider three statistical tests with a p-value to evaluate the performance and goodness of fit of the NTF-Weibull distribution.