Bayesian estimation, Bayesian neural network and maximum likelyhood estimation for a novel transmuted tangent family of distributions with applications in healthcare data

Abstract

Cancer is currently the main cause of primary or secondary premature mortality in most countries. Medical researchers require statistical analysis to identify the most suitable model for assessing the remission periods or survival times of cancer patients, thereby producing precise results. The current study contributes a novel family of distributions to analyze the remission periods or survival times of cancer data effectively, termed the transmuted tangent family of distributions, achieved through the combination of the quadratic transmuted family with the tan-G class of distributions. The primary statistical properties of the proposed family are established. The Bayesian estimation, Bayesian neural network and maximum likelihood estimation methods are employed for parametric estimation of the family. In addition, four members of the family are introduced. The transmuted tangent Lindley distribution is examined, and its fundamental features are established. Three cancer datasets are examined to verify the fit efficiency of the proposed family through the use of various goodness-of-fit measures. We have demonstrated that, compared to many established families, the proposed family offers a better fit to the data sets.