Modelling lifetime data with simple mathematical representations and an ease in obtaining the parameter estimate of survival models are crucial quests pursued by survival researchers. In this paper, we derived and introduced a one-parameter distribution called the Agu-Eghwerido (AGUE) distribution with its simple mathematical representation. The regression model of the AGUE distribution was also presented. Several basic properties of the new distribution, such as reliability measures, mean residual function, median, moment generating function, skewness, kurtosis, coefficient of variation, and index of dispersion, were derived. The estimation of the proposed distribution parameter was based on the maximum likelihood estimation method. The real-life applications of the distribution were illustrated using two real lifetime negatively and positively skewed data sets. The new distribution provides a better fit than the Pranav, exponential, and Lindley distributions for the data sets. The simulation results showed that the increase in parameter values decreases the mean squared error value. Similarly, the mean estimate tends towards the true parameter value as the sample sizes increase.
AGUE distribution, AGUE regression model, moment generating function, means residual function, hazard rate function, survival rate function
Abdal-hameed, M. K., Khaleel, M. A., Abdullah, Z. M., Oguntunde, P. E., Adejumo, A. O., (2018). Parameter estimation and reliability, hazard functions of Gompertz Burr Type XII distribution. Tikrit Journal for Administration and Economics Sciences, 1(41-2), pp. 381–400.
Agu, F. I., Onwukwe, C. E., (2019). Modified Laplace Distribution, Its Statistical Properties and Applications. Asian Journal of Probability and Statistics, pp. 1–14.
Agu, F. I, Francis, R. E., (2018). Comparison of goodness of fit tests for normal distribution. Asian Journal of Probability and Statistics, pp. 1–32.
Bakouch, H. S., Risti´c, M. M., Asgharzadeh, A., Esmaily, L., Al-Zahrani, B. M., (2012). An exponentiated exponential binomial distribution with application. Statistics and Probability Letters, 82(6), pp. 1067–1081.
Eghwerido, J. T., Nzei, L. C., Agu, F. I., (2020). The Alpha Power Gompertz Distribution: Characterization, Properties, and Applications.Sankhya A - The Indian Journal of Statistics, https://doi.org/ 10.1007/s13171-020-00198-0.
Eghwerido, J. T., Oguntunde, P. E., Agu, F. I., (2020). The Alpha Power Marshall-Olkin-G Distribution: Properties, and Applications. Sankhya A - The Indian Journal of Statistics, https://doi.org/10.1007/s13171-020-00235-y.
Eghwerido, J. T., Agu, F. I., (2021). The Shifted Gompertz-G family of Distributions: Properties and Applications. Mathematica Slovaca, Article in the press.
Eghwerido, J. T., Agu, F. I. Ibidoja, J. O., (2021a). The Shifted Exponential-G family of distributions: properties and applications. Journal of Statistics and Management System, https://doi.org/10.1080/09720510.2021.1874130.
Famoye, F., (2019). Bivariate exponentiated-exponential geometric regression model. Statistica Neerlandica, 73(3), 434–450.
Famoye, F., Carl Lee., (2017). Exponentiated-exponential geometric regression model. Journal of Applied Statistics, 44(16), pp. 2963–2977.
Granzotto, D. C. T., Louzada, F., (2015). The transmuted log-logistic distribution: modeling, inference, and an application to a polled tabapua race time up to first calving data. Communications in Statistics-Theory and Methods, 44(16), pp. 3387–3402.
Gómez-Déniz, E., Calderín-Ojeda, E., (2011). The discrete Lindley distribution: properties and applications. Journal of Statistical Computation and Simulation, 81(11), pp. 1405-1416.
Ghitany, M. E., Atieh, B., Nadarajah, S., (2008). Lindley distribution and its application. Mathematics and computers in simulation, 78(4), pp. 493–506.
Ghitany, M. E., Al-Mutairi, D. K., Balakrishnan, N., Al-Enezi, L. J., (2013). Power Lindley distribution and associated inference. Computational Statistics and Data Analysis, 64, pp. 20–33.
Hanagal, D. D., (2006). Bivariate Weibull regression model based on censored samples. Statistical Papers, 47(1), pp. 137–147.
Handique, L., Chakraborty, S., (2016). Beta generated Kumaraswamy-G and other new families of distributions. arXiv preprint arXiv:1603.00634.
Khaleel, M. A., Al-Noor, N. H., Abdal-Hameed, M. K. Marshall Olkin exponential Gompertz distribution: Properties and applications. Periodicals of Engineering and Natural Sciences, 8(1), pp. 298–312.
Khan, M. S., King, R., Hudson, I. L., (2020). Transmuted Burr Type X Distribution with Covariates Regression Modeling to Analyze Reliability Data. American Journal of Mathematical and Management Sciences, 39(2), pp. 99–121.
Lindley D. V., (1958). Fiducial distributions and Bayes’ theorem. Journal of the Royal Statistical Society, Series B, 20, 1(1), pp. 102–107.
Merovci, F., (2013). Transmuted Rayleigh distribution. Austrian Journal of Statistics, 42(1), pp. 21 –31.
Mood AM, Graybill FA, Boes DC., (1974). Introduction to the theory of statistics, 3rd edn. McGraw Hill, New York
Nadarajah, S., Haghighi, F., (2011). An extension of the exponential distribution. Statistics, 45(6), pp. 543–558.
Odom, C. C., Ijomah, M. A., (2019). Odoma Distribution and Its Application. Asian Journal of Probability and Statistics, pp. 1-11.
Oguntunde, P. E., Khaleel, M. A., Ahmed, M. T., Adejumo, A. O., Odetunmibi, O. A., (2017). A New Generalization of the Lomax Distribution with Increasing, Decreasing, and Constant Failure Rate. Modelling and Simulation in Engineering, 2017.
Oguntunde, P. E., Khaleel, M. A., Adejumo, A. O., Okagbue, H. I., (2018). A study of an extension of the exponential distribution using logistic-x family of distributions. International Journal of Engineering and Technology, 7(4), pp. 5467–5471.
Oluyede, B. O., Yang, T., (2014). Generalizations of the inverse Weibull and related distributions with applications. Electronic Journal of Applied Statistical Analysis, 7(1), pp. 94.
Sharma, V. K., Singh, S. K., Singh, U., Merovci, F., (2016). The generalized inverse Lindley distribution: A new inverse statistical model for the study of upside-down bathtub data. Communications in Statistics-Theory and Methods, 45(19), pp. 5709–5729.
Shaked, M., Shanthikumar, J. G., (1994). Stochastic Orders and Their Applications, Academic Press, New York.
Shanker, R., (2015a). Akash distribution and its applications. International Journal of Probability and Statistics, 4(3), pp. 65–75.
Shanker, R., (2016). Aradhana distribution and its Applications. International Journal of Statistics and Applications, 6(1), pp. 23-34.
Shanker, R., Shukla, K. K., (2017). Ishita distribution and its applications. Biometrics and Biostatistics International Journal, 5(2), pp. 1–9.
Shanker, R., (2016). Sujatha distribution and its Applications. Statistics in Transition. New Series, 17(3), pp. 391–410.
Shanker, R., Mishra, A., (2013). On a Size-Biased Quasi Poisson-Lindley Distribution. International Journal of probability and Statistics, 2(2), pp. 28–34.
Shanker, R., Amanuel, A. G., (2013). A new quasi Lindley distribution. International Journal of Statistics and systems, 8(2), pp. 143-156.
Shukla K. K., (2018). Pranav distribution with properties and its applications. Biom Biostat Int J, 7(3), pp. 244–254.
Warahena-Liyanage, G., Pararai, M., (2014). A generalized power Lindley distribution with applications. Asian journal of mathematics and applications, 2014, pp. 1–23.
Zakerzadeh, H., Dolati, A., (2009). Generalized Lindley distribution. Scientific Information Database, 3(2), pp. 13–25.