The Generalized DUS Transformed Log-Normal Distribution and Its Applications to Cancer and Heart Transplant Datasets

Muhammed Rasheed Irshad, Christophe Chesneau, Soman Latha Nitin, Damodaran Santhamani Shibu and Radhakumari Maya
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Muhammed Rasheed Irshad: Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, Kerala, India
Christophe Chesneau: Department of Mathematics, Université de Caen Basse-Normandie, LMNO, UFR de Sciences, F-14032 Caen, France
Soman Latha Nitin: Department of Statistics, University College, Thiruvananthapuram 695 034, Kerala, India
Damodaran Santhamani Shibu: Department of Statistics, University College, Thiruvananthapuram 695 034, Kerala, India
Radhakumari Maya: Department of Statistics, Government College for Women, Thiruvananthapuram 695 014, Kerala, India

Mathematics, 2021, vol. 9, issue 23, 1-22

Abstract: Many studies have underlined the importance of the log-normal distribution in the modeling of phenomena occurring in biology. With this in mind, in this article we offer a new and motivated transformed version of the log-normal distribution, primarily for use with biological data. The hazard rate function, quantile function, and several other significant aspects of the new distribution are investigated. In particular, we show that the hazard rate function has increasing, decreasing, bathtub, and upside-down bathtub shapes. The maximum likelihood and Bayesian techniques are both used to estimate unknown parameters. Based on the proposed distribution, we also present a parametric regression model and a Bayesian regression approach. As an assessment of the longstanding performance, simulation studies based on maximum likelihood and Bayesian techniques of estimation procedures are also conducted. Two real datasets are used to demonstrate the applicability of the new distribution. The efficiency of the third parameter in the new model is tested by utilizing the likelihood ratio test. Furthermore, the parametric bootstrap approach is used to determine the effectiveness of the suggested model for the datasets.

Keywords: log-normal distribution; DUS transformation; maximum likelihood estimation; Bayesian estimation; regression (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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