The Double XRAMA Distribution: Theory and Applications

  • David U. Gideon Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, Awka, Nigeria
  • Precious O. Ibeakuzie Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, Awka, Nigeria
  • Divine-Favour N. Ekemezie Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, Awka, Nigeria
  • Mmesoma P. Nwankwo Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, Awka, Nigeria
  • Dorathy O. Oramulu Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, Awka, Nigeria
  • Harrison O. Etaga Department of Statistics, Faculty of Physical Sciences, Nnamdi Azikiwe University, Awka, Nigeria
Keywords: double XRama distribution, exponential distribution, Rama distribution, XRama

Abstract

In this paper, a new distribution is proposed by a mixture of two distributions; Exponential and Exponential-Rama the proposed distribution is referred to as the Double XRama distribution. It is flexible in modeling lifetime data. The properties of the XRama distribution were derived and an analysis of the behaviour was conducted. The mathematical properties which include moments, the shape of the distribution, Quantile function, hazard function, survival function, stochastic ordering, mean deviation, Bonferroni and Lorenz curve, order statistic, and Renyi entropy have been studied. From the results, the proposed model competes favorably among the members of the XRama class of distributions.

References

Shanker, R. (2016). Sujatha distribution and its applications. Statistics in Transition, new series, 17(3), 391-410. https://doi.org/10.21307/stattrans-2016-029

Lindley, D. V. (1958). Fiducial distributions and Bayes' theorem. Journal of the Royal Statistical Society. Series B (Methodological), 20(1), 102-107. https://doi.org/10.1111/j.2517-6161.1958.tb00278.x

Shanker, R. (2015a). Shanker distribution and its applications. International Journal of Statistics and Applications, 5(6), 338-348.

Shanker, R., & Shukla, K. K. (2017). Power Shanker distribution and its application. Türkiye Klinikleri Biyoistatistik, 9(3), 175-187. https://doi.org/10.5336/biostatic.2017-56601

Ganaie, R. A., Rajagopalan, V., & Aldulaimi, S. (2021). The weighted power Shanker distribution with characterizations and applications of real-life time data. Journal of Statistics Applications & Probability, 10(1), 245-265. https://doi.org/10.18576/jsap/100122

Lemonte, A. J., & Cordeiro, G. M. (2013). An extended Lomax distribution. Statistics, 47(4), 800-816. https://doi.org/10.1080/02331888.2011.568119

Afuecheta, E., Chan, S., & Nadarajah, S. (2019). Flexible models for stock returns based on Student's t distribution. The Manchester School, 87(3), 403-427. https://doi.org/10.1111/manc.12234

Hassan, A. S., & Elgarhy, M. (2016). Kumaraswamy Weibull-generated family of distributions with applications. Advances and Applications in Statistics, 48(3), 205. https://doi.org/10.17654/AS048030205

Bourguignon, M., Silva, R. B., & Cordeiro, G. M. (2014). The Weibull-G family of probability distributions. Journal of Data Science, 12(1), 53-68. https://doi.org/10.6339/JDS.201401_12(1).0004

Hassan, A. S., Elgarhy, M., Mohamd, R. E., & Alrajhi, S. (2019). On the alpha power transformed power Lindley distribution. Journal of Probability and Statistics, 2019. https://doi.org/10.1155/2019/8024769

Nadarajah, S., Bakouch, H. S., & Tahmasbi, R. (2011). A generalized Lindley distribution. Sankhya B, 73(2), 331-359. https://doi.org/10.1007/s13571-011-0025-9

Shukla, K. K. (2018). Pranav distribution with properties and its applications. Biom Biostat Int J, 7(3), 244-254. https://doi.org/10.15406/bbij.2018.07.00215

Shukla, K. K., & Shanker, R. (2019). Shukla distribution and its application. Reliability: Theory & Applications, 14(3), 46-55.

Shanker, R., & Shukla, K. K. (2017). Ishita distribution and its applications. Biometrics & Biostatistics International Journal, 5(2), 1-9. https://doi.org/10.15406/bbij.2017.05.00126

Shanker, R. (2015b). Akash distribution and its applications. International Journal of Probability and Statistics, 4(3), 65-75.

Shanker, R. (2017a). Rani distribution and its application. Biometrics & Biostatistics International Journal, 6(1), 1-10. https://doi.org/10.15406/bbij.2017.06.00155

Shanker, R. (2017b). Rama distribution and its application. International Journal of Statistics and Applications, 7(1), 26-35.

Sen, S., Maiti, S. S., & Chandra, N. (2016). The xgamma distribution: statistical properties and application. Journal of Modern Applied Statistical Methods, 15(1), 38. https://doi.org/10.22237/jmasm/1462077420

Shanker, R. (2016). Aradhana distribution and its applications. International Journal of Statistics and Applications, 6(1), 23-34.

Odom, C. C., & Ijomah, M. A. (2019). Odoma distribution and its application. Asian Journal of Probability and Statistics, 4(1), 1-11. https://doi.org/10.9734/ajpas/2019/v4i130103

Chinedu, E. Q., Asogwa, E. C., Sunday, B. T., Onyeizu, N. M., & Obulezi, J. O. (2023). Unraveling emotions: Contemporary approaches in sentiment analysis. J Sen Net Data Comm, 3(1), 223-230. https://doi.org/10.33140/JSNDC.03.01.14

Anabike, I. C., Igbokwe, C. P., Onyekwere, C. K., & Obulezi, O. J. (2023). Inference on the parameters of Zubair-Exponential distribution with application to survival times of Guinea Pigs. Journal of Advances in Mathematics and Computer Science, 38(7), 12-35. https://doi.org/10.9734/jamcs/2023/v38i71769

Chukwuma, P. O., Harrison, E. O., Ibeakuzie, P., Anabike, I. C., & Obulezi, O. J. (2024). A new reduced quantile function for generating families of distributions. Ann Math Phys, 7(1), 001-015. https://doi.org/10.17352/amp.000103

Etaga, H. O., Onyekwere, C. K., Omeje, I. L., Nwankwo, M. P., Oramulu, D. O., & Obulezi, O. J. (2023). Estimation of the Xrama distribution parameter under complete and progressive type-II censored schemes. Sch J Phys Math Stat, 10, 203-219. https://doi.org/10.36347/sjpms.2023.v10i10.002

Musa, A., Onyeagu, S. I., & Obulezi, O. J. (2023a). Exponentiated power Lindley-Logarithmic distribution and its applications. Asian Research Journal of Mathematics, 19(8), 47-60. https://doi.org/10.9734/arjom/2023/v1918686

Musa, A., Onyeagu, S. I., & Obulezi, O. J. (2023b). Comparative study based on simulation of some methods of classical estimation of the parameters of exponentiated Lindley-Logarithmic distribution. Asian Journal of Probability and Statistics, 22(4), 14-30. https://doi.org/10.9734/ajpas/2023/v2214489

Onyekwere, C. K., & Obulezi, O. J. (2022). Chris-Jerry distribution and its applications. Asian Journal of Probability and Statistics, 20(1), 16-30. https://doi.org/10.9734/ajpas/2022/v20i130480

Etaga, H. O., Nwankwo, M. P., Oramulu, D. O., & Obulezi, O. J. (2023). An improved XShanker distribution with applications to rainfall and vinyl chloride data. Sch J Eng Tech, 9, 212-224. https://doi.org/10.36347/sjet.2023.v11109.005

Etaga, H. O., Celestine, E. C., Onyekwere, C. K., Omeje, I. L., Nwankwo, M. P., Oramulu, D. O., & Obulezi, O. J. (2023). A new modification of Shanker distribution with applications to increasing failure rate data. Earthline Journal of Mathematical Sciences, 13(2), 509-526. https://doi.org/10.34198/ejms.13223.509526

Nwankwo, M. P., Onyeizu, N. M., Asogwa, E. C., Ejike, C. O., & Obulezi, O. J. (2023). Prediction of house prices in Lagos-Nigeria using machine learning models. European Journal of Theoretical and Applied Sciences, 1(5), 313-326. https://doi.org/10.59324/ejtas.2023.1(5).22

Nwankwo, B. C., Orjiakoh, J. N., Nwankwo, M. P., Chukwu, E. I. M. I. C., & Obulezi, O. J. (2024). A new distribution for modeling both blood cancer data and median effective dose (ED50) of Artemether-Lumefantrine against P. falciparum. Earthline Journal of Mathematical Sciences, 14(1), 41-62. https://doi.org/10.34198/ejms.14124.041062

Obulezi, O. J., Ujunwa, O. E., Anabike, I. C., & Igbokwe, C. P. (2023). The exponentiated power Chris-Jerry distribution: properties, regression, simulation and applications to infant mortality rate and lifetime of COVID-19 patients. TWIST, 18(4), 328-337. https://doi.org/10.33552/ABBA.2023.05.000620

Nwankwo, M. P., Onyeizu, N. M., Asogwa, E. C., Ejike, C. O., & Obulezi, O. J. (2023). Prediction of house prices in Lagos-Nigeria using machine learning models. European Journal of Theoretical and Applied Sciences, 1(5), 313-326. https://doi.org/10.59324/ejtas.2023.1(5).22

Nwankwo, B. C., Orjiakoh, J. N., Nwankwo, M. P., Chukwu, E. I. M. I. C., & Obulezi, O. J. (2024). A new distribution for modeling both blood cancer data and median effective dose (ED50) of Artemether-Lumefantrine against P. falciparum. Earthline Journal of Mathematical Sciences, 14(1), 41-62. https://doi.org/10.34198/ejms.14124.041062

Obulezi, O. J., Ujunwa, O. E., Anabike, I. C., & Igbokwe, C. P. (2023). The exponentiated power Chris-Jerry distribution: properties, regression, simulation and applications to infant mortality rate and lifetime of COVID-19 patients. TWIST, 18(4), 328-337. https://doi.org/10.33552/ABBA.2023.05.000620

Obulezi, O. J., Chinedu, E. Q., Oramulu, D. O., Etaga, H. O., Onyeizu, N. М., & Ejike, C. O. (2023). Machine learning models for predicting transportation costs inflated by fuel subsidy removal policy in Nigeria. Int. Res. J. Mod. Eng. Technol. Sci., 5, 1053-1070.

Obulezi, O. J., Anabike, I. C., Oyo, O. G., Igbokwe, C., & Etaga, H. (2023). Marshall-Olkin Chris-Jerry distribution and its applications. International Journal of Innovative Science and Research Technology, 8(5), 522-533.

Obulezi, O., Igbokwe, C. P., & Anabike, I. C. (2023). Single acceptance sampling plan based on truncated life tests for Zubair-exponential distribution. Earthline Journal of Mathematical Sciences, 13(1), 165-181. https://doi.org/10.34198/ejms.13123.165181

Obulezi, O. J., Chidimma, N. N., Igbokwe, C. P., & Anabike, I. C. (2023). Statistical analysis on diagnosed cases of malaria and typhoid fever in Enugu-Nigeria. GSJ, 11(6).

Oha, F. C., Etaga, H. O., Ibeakuzie, P. O., Anabike, I. C., & Obulezi, O. J. (2024). Power XShanker distribution: properties, estimation, and applications. Eng OA, 2(1), 01-20. https://doi.org/10.33140/EOA.01.02.07

Onyekwere, C. K., Okoro, C. N., Obulezi, O. J., Udofia, E. M., & Anabike, I. C. (2022). Modification of Shanker distribution using quadratic rank transmutation map. Journal of Xidian University, 16(8), 179-198. https://doi.org/10.9734/ajpas/2022/v20i130480

Oramulu, D. O., Etaga, H. O., Onuorah, A. J., & Obulezi, O. J. (2023). A new member in the Lindley class of distributions with flexible applications. Sch J Phys Math Stat, 7, 148-159. https://doi.org/10.36347/sjpms.2022.v10i07.002

Nwankwo, B. C., Obiora-Ilouno, H. O., Almulhim, F. A., Mustafa, M. S., & Obulezi, O. J. (2024). Group acceptance sampling plans for type-I heavy-tailed exponential distribution based on truncated life tests. AIP Advances, 14(3). https://doi.org/10.1063/5.0194258

Oramulu, D. O., Igbokwe, C. P., Anabike, I. C., Etaga, H. O., & Obulezi, O. J. (2023). Simulation study of the Bayesian and non-Bayesian estimation of a new lifetime distribution parameters with increasing hazard rate. Asian Research Journal of Mathematics, 19(9), 183-211. https://doi.org/10.9734/arjom/2023/v19i9711

Tolba, A. H., Onyekwere, C. K., El-Saeed, A. R., Alsadat, N., Alohali, H., & Obulezi, O. J. (2023). A new distribution for modeling data with increasing hazard rate: a case of COVID-19 pandemic and vinyl chloride data. Sustainability, 15 (17), 12782. https://doi.org/10.3390/su151712782

Published
2024-03-21
How to Cite
Gideon, D. U., Ibeakuzie, P. O., Ekemezie, D.-F. N., Nwankwo, M. P., Oramulu, D. O., & Etaga, H. O. (2024). The Double XRAMA Distribution: Theory and Applications. Earthline Journal of Mathematical Sciences, 14(3), 477-500. https://doi.org/10.34198/ejms.14324.477500
Section
Articles

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