Versatile Extension of the Unit Gompertz: Efficient Estimation and Application

Abstract

Despite the availability of numerous statistical models for describing real-world data, the need remains for flexible distributions capable of accurately capturing diverse spread patterns, particularly within the unit interval. This study introduces the Kavya-Manoharan (KM)-unit Gompertz (KM-UGo) distribution, a novel model tailored for data confined to the unit interval. By combining the unit Gompertz distribution and the KM transformation, the KM-UGo distribution is an improved version of the existing unit-Gompertz distribution, offering more adaptability and the possibility of better model fit in a a wider range of data with diverse spread patterns. This enhances its ability to model various hazard rate shapes, including J-shaped, bathtub, increasing, inverted bathtub, and decreasing. The paper delves into the mathematical properties of the KM-UGo distribution, deriving key characteristics such as moments, probability-weighted moments, incomplete moments, residual and reversed residual life, quantile function, and entropy measures. Classical estimation techniques, including maximum likelihood, least squares, maximum product spacing, Cramér-von Mises, Anderson-Darling, and weighted least squares are employed to determine the distribution's parameters and the results are assessed using a Monte Carlo method. The study's findings showed that the maximum likelihood and maximum product spacing estimation methods offer more accurate and reliable parameter estimates. Furthermore, as demonstrated in simulation studies, larger sample sizes produce better parameter estimates, which are characterized by lower bias and higher accuracy. To illustrate its practical application, the KM-UGo distribution is applied to two real-world datasets residing within the unit interval.

Keywords

• Kavya and Manoharan
• Unit Gompertz
• Entropy measures
• Parameter estimation
• Goodness of fit tests

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