A CUBIC TRANSMUTED ISHITA DISTRIBUTION: PROPERTIES, SIMULATION AND APPLICATION TO COVID-19 DATA.

Abstract

This study introduces the Cubic Transmuted Ishita Distribution (CuTrID), which is an improvement of the Ishita distribution that was developed by substitution of the Ishita distribution into the cubic transmuted family. The CuTrID provides greater flexibility in modeling positively skewed data. We derived some essential properties of the compound CuTrID, including survival and hazard functions, moments, and generating functions. Parameter estimation was conducted by the method of maximum likelihood estimation, and the performance of the estimators was examined through simulation study under varying sample sizes. The simulation outputs show that the estimators are converging to the true parameters, with decreasing bias and MSE as the sample size increases. We applied the CuTrID distribution to COVID-19 infection data from Nigeria. Some information criteria which include AIC, CAIC, BIC, HQIC, and goodness-of-fit (Kolmogorov-Smirnov) statistics revealed that the CuTrID provides a superior fit over the Ishita distribution (ID), Transmuted Ishita distribution (TrID), and Sine–Ishita distribution (SID). These findings show that CuTrID is a compound distribution that can be used for modeling modern data with increasing failure rates, making it a valuable tool in epidemiological, biomedical, and reliability studies.