The
problem of skewness is common among clinical trials and survival data, which has
been 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 density, cumulative density, reliability rate, hazard
rate, reverse hazard rate, moment generating and 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, CramerVon Misses, Kolmogorov Smirnov (KS), Akaike
Information, Bayesian Information, and
Consistent Akaike Information Criterion is employed
to select the better distribution from those models considered in the work. The
results from the statistics criteria show that the intended
References
[1]
Badmus, N.I., Olanrewaju, F. and Adeniran, A.T. (2020) Modeling Covid-19 Pandemic Data with Beta Double Exponential Distribution. Asian Journal of Research and Infectious Diseases, 5, 66-79. https://doi.org/10.9734/ajrid/2020/v5i430181
[2]
Dey, S.K., Rahman, M.M., Siddiqi, U.R. and Howlader, A. (2020) Analyzing the Epidemiological Outbreak of COVID19: A Visual Exploratory Data Analysis Approach. Journal of Medical Virology, 92, 632-638.
https://doi.org/10.1002/jmv.25743
[3]
World Health Organization (2020) Surveillance Case Definitions for Human Infection with Novel Coronavirus (nCoV).
[4]
Yoo, J.-H. (2020) The Fight against the 2019-nCoV Outbreak: An Arduous March Has Just Begun. Journal of Korean Medical Science, 35, 1598-6357.
https://doi.org/10.3346/jkms.2020.35.e56
[5]
Moharraza, P., Richardson, G. and Richardson, G. (2021) A Mathematical Model for Spread of COVID-19 in the World. Journal of Applied Mathematics and Physics, 9, 1890-1895. https://doi.org/10.4236/jamp.2021.98122
[6]
Zheng, H. and Bonasera, A. (2022) Controlling the World Wide Chaotic Spreading of Covid-19 through Vaccinations. Journal of Modern Physics, 13, 1-15.
https://doi.org/10.4236/jmp.2022.131001
[7]
Fatima, K., Jan, U. and Ahmad, S.P. (2018) Statistical Properties of Rayleigh Lomax Distribution with Applications in Survival Analysis. Journal of Data Scoence, 16, 531-548. https://doi.org/10.6339/JDS.201807_16(3).0005
[8]
Jones, M.C. (2004) Families of Distributions Arising from Distributions of Order Statistics. Test, 13, 1-43. https://doi.org/10.1007/BF02602999
[9]
El-Bassiouny, A.H., Abdoand, N.F and Shahen, H.S. (2015) Exponential Lomax Distribution. International Journal of Computer Applications, 121, 24-29.
https://doi.org/10.5120/21602-4713
[10]
Siddiqui, M.M. (1962) Some Problems Connected with Rayleigh Distributions. Journal of Research of the National Bureau of Standards, 60D, 167-174.
https://doi.org/10.6028/jres.066D.020
[11]
Hosking, J.R.M. (1990) L-Moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics. Journal of the Royal Statistical Society: Series B, 52, 105-124. https://doi.org/10.1111/j.2517-6161.1990.tb01775.x
[12]
Cordeiro, G.M. and de Castro, M. (2011) A New Family of Generalized Distributions. Journal of Statistical Computation and Simulation, 81, 883-898.
https://doi.org/10.1080/00949650903530745
[13]
NCDC (2021) General Fact Sheet-Data as at 11th July, 2021. States with Reported Laboratory Confirmed Covid-19 Cases, Recoveries, Deaths Samples Tested and Active Cases.
[14]
Yap, B.W and Sim, C.H. (2011) Comparisons of Various Types of Normality Tests. Journal of Statistical Computation and Simulation, 81, 2141-2155.
https://doi.org/10.1080/00949655.2010.520163
[15]
Shivam, M (2020) Normality Test with Python in Data Science.
https://medium.com/@shivamrkom?source=post_page........5abbefc81fdo
