The problem of skewness is common among clinical trials and survival data which has being the research focus derivation and proposition of different flexible distributions. Thus, a new distribution called Extended Rayleigh Lomax distribution is constructed from Rayleigh Lomax distribution to capture the excessiveness of some survival data. We derive the new distribution by using beta logit function proposed by Jones (2004). Some statistical properties of the distribution such as probability density function, cumulative density function, reliability rate, hazard rate, reverse hazard rate, moment generating functions, likelihood functions, skewness, kurtosis and coefficient of variation are obtained. We also performed the expected estimation of model parameters by maximum likelihood; goodness of fit and model selection criteria including Anderson Darling (AD), CramerVon Misses (CVM), Kolmogorov Smirnov (KS), Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Consistent Akaike Information Criterion (CAIC) are employed to select the better distribution from those models considered in the work. The results from the statistics criteria show that the proposed distribution performs better with better representation of the States in Nigeria COVID-19 death cases data than other competing models.
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