  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.
