Truncated Exponential Log-Topp-Leone Rayleigh Distributions: Properties with Application to Bladder Cancer Data

Study’s Excerpt/Novelty This study presents a truncated exponential log-topp-leone Rayleigh distribution by expanding the truncated exponential log-topp-leone family of distributions. The study comprehensively analyses the distribution's properties and parameter estimation methods, with practical applications demonstrated using right-skewed bladder cancer data. The new model's superior performance over standard models, evidenced by lower AIC, CAIC, and BIC values, demonstrated its potential in accurately modeling right-skewed data. Full Abstract In this article, we introduce a new truncated exponential log-topp-leone Rayleigh distribution on the basis of the truncated exponential log-topp-leone family of distributions. We discussed some properties, including survival function, hazard function, entropy, moment, moment generating function, quantile, and order statistics. We also estimate the parameters of the distribution using maximum likelihood, least squares, and Cramer von-mises. We demonstrated how suitable the proposed distribution is for modeling right-skewed data, as shown from the pdf plot in Figure 1. Finally, we apply the right-skewed (see Figure 3) bladder cancer data sets and compare the performance of the new model using information criteria (see Table 3), and we conclude that the new model outperforms the other standard models with smaller values of AIC, CAIC, and BIC.