THE ODD RAYLEIGH-G FAMILY OF DISTRIBUTION: PROPERTIES, APPLICATIONS, AND PERFORMANCE COMPARISONS

This study introduces the Odd Rayleigh-G (OR-G) family of distribution and explores its mathematical properties, applications, and performance comparisons. The Odd Rayleigh-Weibull distribution (ORWD) is developed by incorporating the "Odd" transformation into the Rayleigh and Weibull distribution, resulting in a flexible model suitable for various real-life and survival data applications. The probability density function (PDF), cumulative distribution function (CDF), hazard function, and survival function of the ORWD are derived and analyzed. Parameter estimation is performed using the Maximum Likelihood Estimation (MLE) method, and the performance of the ORWD is assessed through simulation studies. The simulations for parameter estimates at 100 sample sizes were conducted and the plot of the simulated data on the PDF, CDF, survival and hazard function demonstrate a comprehensive view of the characteristics of the Odd Rayleigh Weibull distribution. This information is useful for understanding the behaviour of the distribution and for applications in reliability analysis and survival studies. The results demonstrate the consistency and efficiency of the MLE method for the ORWD. The ORWD is compared with other distributions, including the Weibull, Power Rayleigh, and Rayleigh distributions, using goodness-of-fit measures such as the Akaike Information Criterion (AIC = 111.0238 and 87.4294), Bayesian Information Criterion (BIC = 117.2564 and 96.0320), and Kolmogorov-Smirnov (KS = 0.9559 and 0.9889) test with p-values (p-val = 7.772e-16 and 2.2e-16). The ORWD shows superior performance in fitting the mortality dataset and the Reddit advertisement dataset, highlighting its potential for modelling complex data structures. Overall, this study provides a comprehensive framework for the...