Statistical Analysis of Mother-to-Child HIV Transmission Rate Using a Weibull-Exponential Inverse Exponential Distribution

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Adana’a Felix Chama
Emmanuel Remi Omoboriowo
Gerald Ikechukwu Onwuka
Terna Godfrey Ieren


Distribution functions, their properties and interrelationships play a significant role in modeling naturally occurring phenomena. Numerous standard distributions have been extensively used over the past decades for modeling data in several fields, however, generalizing these standard distributions has produced several compound distributions that are more flexible compared to the baseline distributions. Acquired immune deficiency syndrome is a disease caused by human immunodeficiency virus (HIV) that leads to a continuous decay of the human body immune system. Over the past few years, the rate of mother-to-child transmission of HIV has been on a non-decreasing trend in Nigeria and hence becoming a threat to the health of the nation. The Weibull generalized family of distributions has been efficient in developing new continuous probability distributions with additional two shape parameters. In this paper, a Weibull-based model has been proposed and it is called “a Weibull-Exponential Inverse Exponential distribution”. The properties, estimation of parameters and application of the new distribution are presented and discussed in this paper. Adequate application and investigation of the new model was done using a dataset on the rate of mother-to-child transmission of HIV and the result was compared with that of other competing models.

Weibull-G family, Weibull-exponential inverse exponential distribution, properties, maximum likelihood estimation, application.

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How to Cite
Chama, A. F., Omoboriowo, E. R., Onwuka, G. I., & Ieren, T. G. (2021). Statistical Analysis of Mother-to-Child HIV Transmission Rate Using a Weibull-Exponential Inverse Exponential Distribution. International STD Research & Reviews, 10(1), 1-11.
Original Research Article


Cordeiro GM, Afify AZ, Ortega EMM, Suzuki AK, Mead ME. The odd Lomax generator of distributions: Properties, estimation and applications. Journal of Computational and Applied Mathematics. 2019;347:222–237.

Cordeiro GM, Ortega EMM, Popovic BV, Pescim RR. The Lomax generator of distributions: Properties, minification process and regression model. Applied Mathematics and Computation. 2014;247:465-486.

Abdullahi UK, Ieren TG. On the inferences and applications of transmuted exponential Lomax distribution, International Journal of Advanced Probability and Statistics. 2018;6(1):30-36.

Yahaya A, Ieren TG. On Transmuted weibull-exponential distribution: Its properties and applications, Nigerian Journal of Scientific Research. 2017;16(3):289-297.

Afify MZ, Yousof HM, Cordeiro GM, Ortega EMM, Nofal ZM. The Weibull Frechet Distribution and Its Applications. Journal of Applied Statistics. 2016;1-22.

Ieren TG, Kuhe AD. On the Properties and Applications of Lomax-Exponential Distribution. Asian Journal of Probability and Statistics. 2018;1(4):1-13.

Tahir MH, Zubair M, Mansoor M, Cordeiro GM, Alizadeh M. A New Weibull-G family of distributions. Hacettepe Journal of Mathematics and Statistics 2016;45(2):629-647.

Ieren TG, Yahaya A. The Weimal Distribution: its properties and applications. Journal of the Nigeria Association of Mathematical Physics. 2017;39:135-148.

Bourguignon M, Silva RB, Cordeiro GM. The weibull-G family of probability distributions. Journal of Data Science. 2014;12:53-68.

Gomes-Silva F, Percontini A, De Brito E, Ramos MW, Venancio R & Cordeiro GM. The Odd Lindley-G Family of Distributions. Austrian Journal of Statistics. 2017;46:65-87.

Ieren TG, Koleoso PO, Chama AF, Eraikhuemen IB, Yakubu N. A Lomax-inverse lindley distribution: Model, properties and applications to lifetime data. Journal of Advances in Mathematics and Computer Science. 2019;34(3-4):1-28.

Alzaatreh A, Famoye F, Lee C. A new method for generating families of continuous distributions. Metron.. 2013;71: 63–79.

Ieren TG, Kromtit FM, Agbor BU, Eraikhuemen IB, Koleoso PO. A Power Gompertz Distribution: Model, properties and application to bladder cancer data. Asian Research Journal of Mathematics. 2019;15(2):1-14.

Ieren TG, Oyamakin SO, Chukwu AU. Modeling Lifetime Data With Weibull-Lindley Distribution. Biometrics and Biostatistics International Journal. 2018;7(6):532‒544.

Oguntunde PE, Adejumo AO, Owoloko EA. Exponential Inverse Exponential (EIE) distribution with applications to lifetime data, Asian Journal Scientific Research. 2017;10:169-177.

Ieren TG, Abdullahi J. Properties and Applications of a Two-Parameter Inverse Exponential Distribution with a Decreasing Failure Rate. Pakistan Journal of Statistics. 2020;36(3):183-206.

Oguntunde PE, Adejumo AO, Owoloko EA. Application of Kumaraswamy inverse exponential distribution to real lifetime data. International Journal of Applied Mathematics and Statistics. 2017;56(5):34–47

Oguntunde PE, Adejumo AO, Owoloko EA. On the exponentiated generalized inverse exponential distribution-Lecture Notes on engineering and computer science. Proceeding of the World Congress on Engineering. London, UK. 2017;80-83.

Oguntunde PE, Adejumo AO, Okagbue H, IRastogi MK. Statistical Properties and Applications of a New Lindley Exponential Distribution. Gazi University Journal of Science. 2016;29(4):831-838.

Abdullahi J, Abdullahi UK, Ieren TG, Kuhe DA, Umar AA. On the properties and applications of transmuted odd generalized exponential- exponential distribution. Asian Journal of Probability and Statistics. 2018;1(4):1-14.

Owoloko EA, Oguntunde PE, Adejumo AO. Performance rating of the transmuted exponential distribution: an analytical approach. Springerplus 2015;4:818-829.

Oguntunde PE, Adejumo AO. The transmuted inverse exponential distribution. International Journal of Advanced Statistics and Probability. 2015;3(1):1–7.

Maiti SS, Pramanik S. Odds Generalized Exponential-Exponential Distribution. Journal of Data Science. 2015;13:733- 754.

Oguntunde PE, Balogun OS, Okagbue HI, Bishop SA. The Weibull-Exponential Distribution: Its properties and application. Journal of Applied Sciences. 2015;15(11):1305-1311.

Hyndman RJ, Fan Y. Sample quantiles in statistical packages. The American Statistician. 1996;50(4):361-365.

Kenney JF, Keeping ES. Mathematics of Statistics. 3 edn, Chapman & Hall Ltd, New Jersey; 1962.

Moors JJ. A quantile alternative for kurtosis. Journal of the Royal Statistical Society: Series D. 1988;37:25–32.

Burr CK, Lampe MA, Corle S, Margolin FS, Abresh C, Clark J, et al. An end to perinatal HIV: Success in the US requires ongoing and innovative efforts that should expand globally. J Public Health Policy. 2007;28:249-60.

Royal College of Obstetricians and Gynaecologists. Management of HIV in pregnancy. Guideline No. 39. London: RCOG; 2004.

Mofenson LM. Prevention in neglected subpopulations: Prevention of mother-to-child transmission of HIV infection. Clin Infect Dis. 2010;50 Suppl3:S130-48.

Chen G, Balakrishnan N. A general purpose approximate goodness-of-fit test. Journal of Quality Technology. 1995;27:154–161.