As an extension of the modified Weibull (MW) model, a novel three-parameter lifetime distribution known as the sine modified Weibull (SMW) model is developed and examined. The statistical features of the SMW model, such as the quantile function, moments, moment generating function, and incomplete moment, are computed. The maximum likelihood approach of statistical inference is utilized to estimate the SMW distribution parameters. Applications to COVID-19 real data sets demonstrate the flexibility of the SMW model by comparing it to well-known models such as exponentiated exponential Weibull (EEW), exponentiated Kumaraswamy Weibull (EKW), exponentiated truncated inverse Weibull inverse Weibull (ETIWIW), and weighted exponentiated inverted Weibull (WEIW).

modified Weibull distribution, sine generated class, incomplete moments, COVID-19, maximum likelihood.

Received: February 9, 2022; Revised: March 26, 2022; Accepted: March 30, 2022

How to cite this article: I. Elbatal, Naif Alotaibi, Ibrahim Al-Dayel, A. W. Shawki and M. Elgarhy, Statistical analysis of COVID-19 data in Kingdom of Saudi Arabia using: sine modified Weibull model, JP Journal of Biostatistics 20 (2022), 11-26.

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] G. M. Cordeiro and M. de Castro, A new family of generalized distributions, J. Stat. Comput. Simul. 81 (2011), 883-893.
[2] K. Zografos and N. Balakrishnan, On families of beta- and generalized gamma-generated distributions and associated inference, Stat. Methodol. 6(4) (2009), 344-362.
[3] A. Alzaghal, F. Felix Famoye and C. Lee, Exponentiated T-X family of distributions with some applications, International Journal of Statistics and Probability 2(3) (2013), 31-49.
[4] D. Kumar, U. Singh and S. K. Singh, A new distribution using sine function - its application to bladder cancer patients data, Journal of Statistics Applications and Probability 4(3) (2015), 417-427.
[5] F. S. Gomes-Silva, A. Percontini, E. de Brito, M. W. Ramos, R. Venâncio and G. M. Cordeiro, The odd Lindley-G family of distributions, Austrian Journal of Statistics 46(1) (2017), 65-87.
[6] A. S. Hassan, M. Elgarhy and M. Shakil, Type II half logistic family of distributions with applications, Pakistan Journal of Statistics and Operation Research 13(2) (2017), 245-264.
[7] M. Nassar, D. Kumar, S. Dey, G. M. Cordeiro and A. Z. Afify, The Marshall-Olkin alpha power family of distributions with applications, J. Comput. Appl. Math. 351 (2019), 41-53.
[8] M. Bourguignon, R. B. Silva and G. M. Cordeiro, The Weibull-G family of probability distributions, Journal of Data Science 12 (2014), 53-68.
[9] A. Z. Afify, G. M. Cordeiro, H. M. Yousof, Z. M. Nofal and A. Alzaatreh, The Kumaraswamy transmuted-G family of distributions: properties and applications, Journal of Data Science 14(2) (2016), 245-270.
[10] A. S. Hassan and S. E. Hemeda, The additive Weibull-G family of probability distributions, International Journal of Mathematics and its Applications 4 (2016), 151-164.
[11] R. A. Bantan, F. Jamal, Ch. Chesneau and M. Elgarhy, A new power Topp-Leone generated family of distributions with applications, Entropy 21(12) (2019), 1-24.
[12] M. A. Aldahlan, F. Jamal, Ch. Chesneau, M. Elgarhy and I. Elbatal, The truncated Cauchy power family of distributions with inference and applications, Entropy 22 (2020), 1-25.
[13] G. M. Cordeiro, A. Z. Afify, E. M. Ortega, A. K. Suzuki and M. E. Mead, The odd Lomax generator of distributions: properties, estimation and applications, J. Comput. Appl. Math. 347 (2019), 222-237.
[14] M. M. Badr, I. Elbatal, F. Jamal, Ch. Chesneau and M. Elgarhy, The transmuted odd Fréchet-G family of distributions: theory and applications, Mathematics 8 (2020), 1-20.
[15] A. A. Al-Babtain, I. Elbatal, Ch. Chesneau and M. Elgarhy, Sine Topp-Leone-G family of distributions: theory and applications, Open Physics 18 (2020), 574-593.
[16] A. M. Sarhan and M. Zaindin, Modified Weibull distribution, Appl. Sci. 11 (2009), 123-136.
[17] G. O. Silva, E. M. M. Ortega and G. M. Cordeiro, Beta modified Weibull distribution, Lifetime Data Analysis 16(3) (2010), 409-430.
[18] S. J. Almalki and J. Yuan, A new modified Weibull distribution, Reliability Engineering and System Safety 111 (2013), 164-170.
[19] G. M. Cordeiro, A. Saboor, M. N. Khan, S. B. Provost and E. M. M. Ortega, The transmuted generalized modified Weibull distribution, Filomat 31(5) (2017), 1395-1412.
[20] M. S. Khan and R. King, Transmuted modified Weibull distribution: a generalization of the modified Weibull probability distribution, European Journal of Pure and Applied Mathematics 6 (2013), 66-88.
[21] I. Elbatal, Exponentiated modified Weibull distribution, Econ. Qual. Control 26 (2011), 189-200.
[22] A. Saboor, H. S. Bakouch and M. N. Khan, Beta Sarhan-Zaindin modified Weibull distribution, Appl. Math. Model. 40 (2016), 6604-6621.
[23] B. He and W. Cui, An additive modified Weibull distribution, Reliability Engineering and System Safety 145 (2016), 28-37.
[24] D. Al-Sulami, Exponentiated exponential Weibull distribution: mathematical properties and application, American Journal of Applied Sciences 17(1) (2020), 188-195.
[25] F. H. Eissa, The exponentiated Kumaraswamy-Weibull distribution with application to real data, International Journal of Statistics and Probability 6(6) (2017), 167-182.
[26] A. M. Almarashi, M. Elgarhy, F. Jamal and C. Chesneau, The exponentiated truncated inverse Weibull-generated family of distributions with applications, Symmetry 12(4) (2020), 650. https://doi.org/10.3390/sym12040650.
[27] A. Saghira, S. Tazeema and I. Ahmad, The weighted exponentiated inverted Weibull distribution: properties and application, Journal of Informatics and Mathematical Sciences 9(1) (2017), 137-151.