Abstract
Beta distribution has been widely used in many scientific areas. It is applied very often and is known as a probability distribution with wide application in the management of various kinds of problems, such as in survival analysis. In recent years, development has focused on new probabilistic techniques for building new distributions, (e.g., Jones’ Generalized Beta Distribution, 2004). This study will investigate the statistical properties of the proposed distribution using six parameters; this is called the Beta Gompertz Generalized Makeham distribution. It includes verifying the probability density function, the cumulative density function, and the hazard function.
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References
Abramowitz, M., & Stegun, I. (2006). Handbook of mathematical functions. Washington, DC: US Government Printing Office. Eq, 9(3), 366.
Akinsete, A., Famoye, F., & Lee, C. (2008). The beta-Pareto distribution. Statistics, 42(6), 547–563.
Andreopoulos, P., & Bersimis, G. F. (2015). Mortality modelling using probability distributions. SCinTE, 1, 189.
Andreopoulos, P., Bersimis, G. F., Tragaki, A., & Rovolis, A. (2019). Mortality modeling using probability distributions. Application in Greek mortality data. Communications in Statistics-Theory and Methods, 48(1), 127–140.
Barreto-Souza, W., Santos, A. H., & Cordeiro, G. M. (2010). The beta generalized exponential distribution. Journal of Statistical Computation and Simulation, 80(2), 159–172.
Castellares, F., & Lemonte, A. J. (2019). On the moments of the generalized Gompertz distribution. Applied Mathematical Modelling, 72, 420–424.
Currie, I. D., Durban, M., & Eilers, P. H. (2004). Smoothing and forecasting mortality rates. Statistical Modelling, 4(4), 279–298.
Eugene, N., Lee, C., & Famoye, F. (2002). Beta-normal distribution and its applications. Communications in Statistics-Theory and Methods, 31(4), 497–512.
Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London, 115, 513–583.
Gupta, A. K., & Nadarajah, S. (2004). Handbook of beta distribution and its applications. Boca Raton: CRC Press.
Jones, J. H. (2005). Mathematical hazards models and model life tables, Stanford Summer Short Course, URL: http://www.stanford.edu/~jhj1/teachingdocs/Jones-mortmodel2005.pdf
Nadarajah, S., & Kotz, S. (2004). The beta Gumbel distribution. Mathematical Problems in Engineering, 2004(4), 323–332.
Nadarajah, S., & Kotz, S. (2006). The beta exponential distribution. Reliability Engineering & System Safety, 91(6), 689–697.
Papaioannou, T. (2001). On distances and measures of information: A case of diversity. Probability and Statistical Models with applications, 503–515.
Tragaki, A., & Panagiotakos, D. (2018). Population ageing and cardiovascular health: The case of Greece. Hellenic Journal of Cardiology, 59, 360–361.
Venter, G. (1983). Transformed beta and gamma distributions and aggregate losses. Proceedings of the Casualty Actuarial Society, 70(133 & 134), 289–308.
Zografos, K., & Balakrishnan, N. (2009). On families of beta- and generalized gamma-generated distributions and associated inference. Statistical Methodology, 6, 344–362.
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Andreopoulos, P., Tragaki, A., Antonopoulos, G., Bersimis, F.G. (2020). Properties and Dynamics of the Beta Gompertz Generalized Makeham Distribution. In: Skiadas, C.H., Skiadas, C. (eds) Demography of Population Health, Aging and Health Expenditures. The Springer Series on Demographic Methods and Population Analysis, vol 50. Springer, Cham. https://doi.org/10.1007/978-3-030-44695-6_18
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DOI: https://doi.org/10.1007/978-3-030-44695-6_18
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