ITM Web Conf.
Volume 61, 2024The 9th International Symposium on Current Progress in Mathematics and Sciences 2023 (The 9th ISCPMS 2023) in conjunction with AUA Academic Conference on the Application of Artificial Intelligences and Data Sciences in a Modern Science for a Better Life
|Number of page(s)
|10 January 2024
Alpha power inverse Weibull distribution: A new lifetime distribution with application to gastric cancer data
Department of Mathematics, Faculty of Mathematics and Natural Sciences (FMIPA), Universitas Indonesia, Depok 16424, Indonesia
* Corresponding author: firstname.lastname@example.org
Lifetime data analysis has an essential role in various fields of science. In general, lifetime data have a skewed distribution pattern. The Weibull distribution is one of the most frequently used distributions for modeling lifetime data. However, the Weibull distribution is not suitable for modeling data with non-monotonous hazard functions, one of which is an upside-down bathtub shape. According to Sharma et al. (2015), the inverse version of several probability distributions can model the data with an upside-down bathtub shape, one of which is the inverse Weibull distribution. This paper explains the Alpha Power Inverse Weibull (APIW) distribution as a generalization version of the inverse Weibull distribution. This distribution is constructed by using the Alpha Power Transformation method. The modification is done by adding a shape parameter to the inverse Weibull distribution to increase flexibility. The characteristics of APIW distribution discussed include probability density function, distribution function, survival function, hazard function, and the r-th moment. The probability density function of APIW distribution is left-skewed and unimodal. In addition, the hazard function of APIW distribution has an upside-down bathtub shape. The parameters of this distribution are estimated by the maximum likelihood method. Finally, for illustration purposes, the data about the time until gastric cancer patients die are modelled with the inverse Weibull distribution, and the APIW distribution is given. The modeling result shows that the Alpha Power Inverse Weibull distribution is better at modeling the time until gastric cancer patients die data than the inverse Weibull distribution.
Key words: Alpha Power Transformation / hazard function / inverse Weibull distribution / lifetime data / maximum likelihood method
© The Authors, published by EDP Sciences, 2024
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