Generalized DUS Transformed Garima Distribution: Properties, Simulations and Applications

• Published in: Lobachevskii journal of mathematics Vol. 44; no. 2; pp. 803 - 814
• Main Author: Akkanphudit, Thanasate
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.02.2023; Springer Nature B.V
• Subjects: Algebra; Analysis; Error reduction; Geometry; Mathematical Logic and Foundations; Mathematics; Mathematics and Statistics; Maximum likelihood estimators; Probability Theory and Stochastic Processes; Simulation; Garima distribution; DUS transformation; Anderson–Daring estimation; generalized DUS transformation; maximum likelihood estimation; lifetime data
• ISSN: 1995-0802; 1818-9962
• DOI: 10.1134/S199508022302004X

Many studies have underlined the importance of the Garima distribution in modeling lifetime data. In this article, we proposed a new distribution using a generalized DUS transform for the Garima distribution. The hazard rate, quantile function, and other significant aspects of the new distribution are investigated. In particular, we show that the hazard rate function has to increase, decrease and upside-down bathtub shapes. The maximum likelihood (ML) and Anderson-Daring (AD) techniques are used to estimate unknown parameters. Simulation studies based on the ML and AD techniques for estimation procedures of the proposed distribution are also conducted. Simulation study results show that ML and AD estimators of the proposed model are asymptotically unbiased, and mean square error reduces by increasing the sample size. Two real datasets are used to demonstrate the applicability of the new distribution.