Discrete Erlang-2 distribution and its application to leukemia and COVID-19

Mohamed Ahmed Mosilhy; Mohamed Ahmed Mosilhy

doi:10.3934/math.2023520

AIMS Mathematics

2023, Volume 8, Issue 5: 10266-10282. doi: 10.3934/math.2023520

Previous Article Next Article

Research article

Discrete Erlang-2 distribution and its application to leukemia and COVID-19

Mohamed Ahmed Mosilhy ^{1,2
,
,}

1.
Department of Mathematics, Faculty of Science, Cairo University, Egypt
2.
Department of Statistics, Faculty of Science, University of Tabuk, KSA

Received: 21 October 2022 Revised: 15 February 2023 Accepted: 20 February 2023 Published: 28 February 2023
MSC : 37M15, 30G25, 44A55

Via the survival discretization method, this research revealed a novel discrete one-parameter distribution known as the discrete Erlang-2 distribution (DE2). The new distribution has numerous surprising improvements over many conventional discrete distributions, particularly when analyzing excessively dispersed count data. Moments and moments-generating functions, a few descriptive measures (central tendency and dispersion), monotonicity of the probability mass function, and the hazard rate function are just a few of the statistical aspects of the postulated distribution that have been developed. The single parameter of the DE2 distribution was estimated via the maximum likelihood technique. Real-world datasets, leukemia and COVID-19, were applied to analyze the effectiveness of the recommended distribution.
- leukemia and COVID-19 data,
- discretization,
- reliability analysis,
- Erlang-2 distribution,
- maximum likelihood estimator,
- Fano factor
Citation: Mohamed Ahmed Mosilhy. Discrete Erlang-2 distribution and its application to leukemia and COVID-19[J]. AIMS Mathematics, 2023, 8(5): 10266-10282. doi: 10.3934/math.2023520

Related Papers:

Abstract

Via the survival discretization method, this research revealed a novel discrete one-parameter distribution known as the discrete Erlang-2 distribution (DE2). The new distribution has numerous surprising improvements over many conventional discrete distributions, particularly when analyzing excessively dispersed count data. Moments and moments-generating functions, a few descriptive measures (central tendency and dispersion), monotonicity of the probability mass function, and the hazard rate function are just a few of the statistical aspects of the postulated distribution that have been developed. The single parameter of the DE2 distribution was estimated via the maximum likelihood technique. Real-world datasets, leukemia and COVID-19, were applied to analyze the effectiveness of the recommended distribution.

References

[1]	C. Bracquemond, O. Gaudoin, A survey on discrete lifetime distribution, Int. J. Reliab. Qual. Saf. Eng., 10 (2003), 69–98. http://doi.org/10.1142/S0218539303001007 doi: 10.1142/S0218539303001007
[2]	S. Chakraborty, Generating discrete analogues of continuous probability distributions-a survey of methods and constructions, J. Stat. Distrib. Appl., 2 (2015), 6. http://doi.org/10.1186/s40488-015-0028-6 doi: 10.1186/s40488-015-0028-6
[3]	D. Roy, The discrete normal distribution, Commun. Stat. Theory Meth., 32 (2003), 1871–1883. http://doi.org/10.1081/STA-120023256 doi: 10.1081/STA-120023256
[4]	H. Krishna, P. S. Pundir, Discrete Burr and discrete Pareto distributions, Stat. Meth., 6 (2009), 177–188. http://doi.org/10.1016/j.stamet.2008.07.001 doi: 10.1016/j.stamet.2008.07.001
[5]	S. Chakraborty, D. Chakravarty, Discrete Gamma distribution: properties and parameter estimations, Commun. Stat. Theory Meth., 41 (2012), 3301–3324. http://doi.org/10.1080/03610926.2011.563014 doi: 10.1080/03610926.2011.563014
[6]	V. Nekoukhou, M. H. Alamatsaz, H. Bidram, Discrete generalized exponential distribution of a second type, J. Theor. Appl. Stat., 47 (2013), 876–887. http://doi.org/10.1080/02331888.2011.633707 doi: 10.1080/02331888.2011.633707
[7]	V. Nekoukhou, H. Bidram, The exponentiated discrete Weibull distribution, Sort Stat. Oper. Res. Trans., 39 (2015), 127–146.
[8]	M. H. Alamatsaz, S. Dey, T. Dey, S. S. Harandi, Discrete generalized Rayleigh distribution, Pak. J. Stat., 32 (2016), 1–20.
[9]	T. Hussain, M. Aslam, M. Ahmad, A two parameter discrete lindley distribution, Rev. Colomb. Estad., 39 (2016), 45–61. http://doi.org/10.15446/rce.v39n1.55138 doi: 10.15446/rce.v39n1.55138
[10]	P. Khongthip, M. Patummasut, W. Bodhisuwan, The discrete weighted exponential distribution and its applications, Songklanakarin J. Sci. Technol., 40 (2018), 1105–1114. http://doi.org/10.14456/sjst-psu.2018.137 doi: 10.14456/sjst-psu.2018.137
[11]	K. Jayakumar, M. G. Babu, Discrete additive Weibull geometric distribution, J. Stat. Theory Appl., 18 (2019), 33–45. http://doi.org/10.2991/jsta.d.190306.005 doi: 10.2991/jsta.d.190306.005
[12]	E. Altun, M. El-Morshedy, 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.
[13]	M. S. Eliwa, Z. A. Alhussain, M. El-Morshedy, Discrete Gompertz-G family of distributions for over- and under-dispersed data with properties, estimation, and applications, Mathematics, 8 (2020), 358. http://doi.org/10.3390/math8030358 doi: 10.3390/math8030358
[14]	A. S. Eldeeb, M. Ahsan-ul-Haq, A. Baba, A discrete analog of inverted Topp-Leone distribution: properties, estimation and applications, Int. J. Anal. Appl., 19 (2021), 695–708. http://doi.org/10.28924/2291-8639-19-2021-695 doi: 10.28924/2291-8639-19-2021-695
[15]	A. R. El-Alosey, Discrete Erlang-truncated exponential distribution, Int. J. Stat. Appl. Math., 6 (2021), 230–236. http://doi.org/10.22271/maths.2021.v6.i1c.653 doi: 10.22271/maths.2021.v6.i1c.653
[16]	M. Ahsan-ul-Haq, A. Babar, S. S. Hashmi, A. S. Alghamd, A. Z. Afify, The discrete type-Ⅱ half-logistic exponential distribution with applications to COVID-19 data, Pak. J. Stat. Oper. Res., 17 (2021), 921–932. http://doi.org/10.18187/pjsor.v17i4.3772 doi: 10.18187/pjsor.v17i4.3772
[17]	A. R. El-Alosey, H. Eledum, Discrete extended Erlang-truncated exponential distribution and its applications, Appl. Math. Inf. Sci., 16 (2021), 127–138. http://doi.org/10.18576/amis/160113 doi: 10.18576/amis/160113
[18]	D. Roy, Reliability measures in the discrete bivariate set-up and related characterization results for a bivariate geometric distribution, J. Multivar. Anal., 46 (1993), 362–373. http://doi.org/10.1006/jmva.1993.1065 doi: 10.1006/jmva.1993.1065
[19]	M. Xie, O. Gaudoin, C. Bracquemond, Redefining failure rate function for discrete distribution, Int. J. Reliab. Qual. Saf. Eng., 9 (2002), 75–85. http://doi.org/10.1142/S0218539302000822 doi: 10.1142/S0218539302000822
[20]	M. Bebbington, C. D. Lai, M. Wellington, R. Zitikis, The discrete additive Weibull distribution: a bathtub-shaped hazard for discontinuous failure data, Reliab. Eng. Syst. Saf., 106 (2012), 37–44. http://doi.org/10.1016/j.ress.2012.06.009 doi: 10.1016/j.ress.2012.06.009
[21]	P. L. Gupta, R. C. Gupta, R. C. Tripathi, On the monotonic properties of discrete failure rates, J. Stat. Plann. Infer., 65 (1997), 55–68. http://doi.org/10.1016/S0378-3758(97)00064-5 doi: 10.1016/S0378-3758(97)00064-5
[22]	U. Fano, Ionization yield of radiations. Ⅱ. The fluctuations of the number of ions, Phys. Rev., 72 (1974), 26–29. http://doi.org/10.1103/PhysRev.72.26 doi: 10.1103/PhysRev.72.26
[23]	E. A. Gehan, Estimating survival functions from the life table, J. Chronic Dis., 21 (1969), 629–644. http://doi.org/10.1016/0021-9681(69)90035-6 doi: 10.1016/0021-9681(69)90035-6
[24]	J. F. Lawless, Statistical models and methods for lifetime data, John Wiley Sons Inc., 2002. http://doi.org/10.1002/9781118033005
[25]	E. Freireich, E. Gehan, E. Frei, L. Schroeder, I. Wolman, R. Anbari, et al., The effect of 6-mercaptopurine on the duration of steroid induced remission in acute leukemia, Blood, 21 (1963), 699–716. http://doi.org/10.1182/blood.V21.6.699.699 doi: 10.1182/blood.V21.6.699.699
[26]	J. P. Klein, M. L. Moeschberger, Survival analysis, Springer Verlag, 1997.
[27]	K. Aramidis, An EM algorithm for estimating negative binomial parameters, Aust. New Z. J. Stat., 41 (1999), 213–221. http://doi.org/10.1111/1467-842X.00075 doi: 10.1111/1467-842X.00075
[28]	P. C. Consul, G. C. Jain, A generalization of the Poisson distribution, Technometrics, 15 (1973), 791–799. http://doi.org/10.2307/1267389 doi: 10.2307/1267389
[29]	E. M. Almetwally, G. M. Ibrahim, Discrete Alpha power inverse Lomax distribution with application of COVID-19 data, Int. J. Appl. Math., 9 (2020), 49–60.

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)