Formulation of Kumaraswamy Generalized Inverse Lomax Distribution

Abstract

Lifetime data is a type of data that consists of a waiting time until an event occurs and modelled by numerous distributions. One of its characteristics that is interesting to be studied is the hazard function due to the flexibility that it has compared to other characteristics of distribution. Inverse Lomax (IL) distribution is one of the distributions considered to have advantages in modelling hazard shape and extended in several ways to address the problem of non-monotone hazard which is often encountered in real life data. However, it needs to be extended to another family of distribution to increase its modelling potential and Kumaraswamy Generalized (KG) family of distribution is used as it adds two more parameters to the distribution. The newly developed distribution is called the Kumaraswamy Generalized Inverse Lomax (KGIL) distribution. The main characteristics of KGIL distribution will be derived, such as cumulative distribution function (cdf), probability density function (pdf), hazard function, and survival function. Maximum likelihood method will also be used to estimate the parameters. The application of the new model is based on head-and-neck cancer lifetime data set. The modelling results show that the KGIL distribution is the best to capture important details of the data set considered