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In this study, a discrete inverted Topp-Leone (DITL) distribution is proposed by utilizing the survival discretization approach. The proposed distribution's mathematical features were derived. The maximum likelihood (ML), method of least squares (LS), weighted least squares (WLS), and Cramer Von-Mises (CVM) estimation techniques were used to estimate the parameter. The theoretical results of the ML, LS, WLS, and CVM estimators were demonstrated via a comprehensive simulation study. The proposed DITL distribution has been applied to analyze two count data sets number of deaths due to Covid-19 in Pakistan and India and the findings show the relevance of the proposed distribution.
- M. Ahsan-ul-Haq, M. Ahmed, J. Zafar, and P. L. Ramos, Modeling of COVID”‘19 Cases in Pakistan Using Lifetime, Ann. Data Sci. (2021), https://doi.org/10.1007/s40745-021-00338-9.
- A. A. Al-Babtain, Abdul Hadi N. Ahmed, and A. Z. Afify, A New Discrete Analog of the Continuous Lindley Distribution, with Reliability Applications, Entropy, 22(6) (2020), 603.
- E. M. Almetwally, H. M. Almongy and H. A. Saleh, Managing risk of spreading “COVID-19” in Egypt: Modelling using a discrete Marshall-Olkin generalized exponential distribution, Int. J. Probab. Stat. 9(2) (2020), 33-41.
- E. M. Almetwally, and G. M. Ibrahim, Discrete Alpha Power Inverse Lomax Distribution with Application of COVID-19 Data, Int. J. Appl. Math. 9(6) (2020), 11-22.
- B. Milan, Estimation of the Final Size of the Second Phase of the Coronavirus COVID 19 Epidemic by the Logistic Model. MedRxiv (Preprint), (2020b), https://doi.org/10.1101/2020.03.11.20024901.
- I. Nesteruk, Statistics Based Predictions of Coronavirus 2019-NCoV Spreading in Mainland China, MedRxiv, (2020), https://doi.org/10.1101/2020.02.12.20021931.
- B. Milan, Estimation of the Final Size of the COVID-19 Epidemic. MedRxiv, (2020), https://doi.org/10.1101/2020.02.16.20023606.
- M. Maleki, M. R. Mahmoudi, D. Wraith, and K. Pho, Time series modelling to forecast the confirmed and recovered cases of COVID-19, Travel Med. Infect. Dis. 37 (2020), 101742.
- G. M. Ibrahim, and E. M. Almetwally, Discrete Marshall-Olkin Lomax Distribution Application of COVID-19, Biomed. J. Sci. Techn. Res. 32(5) (2021), 25381-25390.
- S. Chakraborty, Generating Discrete Analogues of Continuous Probability Distributions-A Survey of Methods and Constructions, J. Stat. Distrib. Appl. 2 (2015), 6.
- T. Nakagawa, and S. Osaki, The discrete Weibull distribution. IEEE Trans. Reliab. 24(5) (1975), 300-301.
- Roy, Dilip. Discrete Rayleigh distribution, IEEE Trans. Reliab. 53(2) (2004), 255-260.
- H. Krishna, and P. S. Pundir, Discrete Burr and Discrete Pareto Distributions, Stat. Methodol. 6(2) (2009), 177-88.
- M. A. Jazi, D. L. Chin, and H. A. Mohammad, A Discrete Inverse Weibull Distribution and Estimation of Its Parameters. Stat. Methodol. 7(2) (2010), 121-32.
- E. GÃ³mez-Déniz, and C. Enrique, The Discrete Lindley Distribution: Properties and Applications, J. Stat. Comput. Simul. 81(11) (2010), 1405-16.
- M. H. Alamatsaz, S. Dey, T. Dey and S. S. Harandi, Discrete Generalized Rayleigh Distribution, Pak. J. Stat. 32(1) (2016), 1-20.
- E. Altun, M. El-Morshedy, and M. S. Eliwa, A Study on Discrete Bilal Distribution With Properties and Applications on integer-valued Autoregressive Process, Revstat. Stat. J. 18 (2020), 70-99.
- M. Shafqat, S. Ali, I. Shah and S. Dey, Univariate Discrete Nadarajah and Haghighi Distribution: Properties and Different Methods of Estimation, Statistica, 80(3) (2020), 301-330.
- M. El-Morshedy, M. S. Eliwa, and E. Altun, Discrete Burr-Hatke Distribution with Properties, Estimation Methods and Regression Model, IEEE Access, 8 (2020), 74359-70.
- A. S. Hassan, M. Elgarhy and R. Ragab, Statistical properties and estimation of inverted Topp-Leone distribution, J. Stat. Appl. Probab. 9(2) (2020), 319-331.
- T. Hussain, and M. Ahmad, Discrete Inverse Rayleigh Distribution, Pak. J. Stat. 30(2) (2014), 203-222.