Exploring the New Sine Unit Gompertz Distribution: Theory, Inference, and Practical Relevance to Financial and Medical Analytics
DOI:
https://doi.org/10.56532/mjsat.v6i2.689Keywords:
Unit Gompertz Distribution, New Sine-G family, Trade share data, Estimations, Hazard rates, Relief times dataAbstract
This study proposes the New Sine Unit Gompertz distribution (NSUGD), a flexible bounded lifetime model derived from the Unit Gompertz distribution. The probability density function accommodates decreasing, near-symmetric, right-skewed, and left-skewed shapes, while the hazard rate function exhibits increasing, J-shaped, or bathtub forms, enabling effective modelling of unit-interval data across diverse applications. Some statistical properties are derived, including the survival and hazard rate functions, quantile function, moments, median, mean, skewness, and kurtosis. Parameters are estimated via maximum likelihood, maximum product of spacings, and Cramér-von Mises methods; a Monte Carlo simulation study, evaluating average estimates and mean squared error, identifies maximum likelihood as the most efficient approach. Empirical validation on financial and medical datasets demonstrates the NSUGD’s superior fit relative to competitors such as the Unit Gompertz, Kumaraswamy, and beta distributions, as evidenced by lower AIC and BIC values and non-significant Kolmogorov-Smirnov statistics with higher p-values. Owing to its adaptability, the NSUGD holds promise for diverse fields, including engineering, insurance, environmental science, and other disciplines where unit bounded data are prevalent.
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