In probability theory, the mixture distribution M has a density function for the collection of random variables and weighted by wi ≥ 0 and . These mixed distributions are used in various disciplines and aim to enrich the collection distribution to more parameters. A more general mixture is derived by Kadri and Halat, by proving the existence of such mixture by wi ∈ R, and maintaining . Kadri and Halat provided many examples and applications for such new mixed distributions. In this paper, we introduce a new mixed distribution of the Generalized Erlang distribution, which is derived from the Hypoexponential distribution. We characterize this new distribution by deriving simply closed expressions for the related functions of the probability density function, cumulative distribution function, moment generating function, reliability function, hazard function, and moments.
References
[1]
Shittu, O.I. and Adepoju, K.A. (2013) On the Beta-Nakagami Distribution. Progress in Applied Mathematics, 5, 49-58.
[2]
Mansoor, M., Tahir, M.H., Alzaatreh, A., Cordeiro, G.M., Zubair, M. and Ghazali, S.S. (2016) An Extended Frechet Distribution: Properties and Applications. Journal of Data Science, 14, 167-188. https://doi.org/10.6339/JDS.201601_14(1).0010
[3]
Kadri, T. and Halat, A. (2022) The New Mixed Hypoexponential-G Family. arXiv: 2211.06585.
[4]
Smaili, K., Kadri, T. and Kadry, S. (2013) Hypoexponential Distribution with Different Parameters. Applied Mathematics, 4, 624-631. https://doi.org/10.4236/am.2013.44087
[5]
Gnedenko, B.V. and Kovalenko, I.N. (1989) Introduction to Queueing Theory. Birkhauser Boston Inc, Boston. https://doi.org/10.1007/978-1-4615-9826-8
[6]
Warsono, W. (2009) Moment Properties of the Generalized Gamma Distribution. In Seminar Nasional Sains, Matematika, Informatika dan Aplikasinya VI UNILA, Fak. Mipa Universitas Lampung, 157-162.
[7]
Temme, N.M. (1996) Special Functions: An Introduction to the Classical Functions of Mathematical Physics. John Wiley & Sons, New York. https://doi.org/10.1002/9781118032572
[8]
Smaili, K., Kadri, T. and Kadry, S. (2014) A Modified-Form Expressions for the Hypoexponential Distribution. British Journal of Mathematics & Computer Science, 4, 322-332. https://doi.org/10.9734/BJMCS/2014/6317
![\"\"](\"Edit_80be65bb-e825-4135-93e4-e81f25c74496.bmp\")
for the collection of random variables ![\"\"](\"Edit_6798ad25-2dec-4a57-b312-780f4fe6996d.bmp\")
and weighted by wi ≥ 0 and ![\"\"](\"Edit_5e1309bc-b0b0-4b98-84d0-babcbcc5f0ba.bmp\")
. These mixed distributions are used in various disciplines and aim to enrich the collection distribution to more parameters. A more general mixture is derived by Kadri and Halat, by proving the existence of such mixture by wi ∈ R, and maintaining ![\"\"](\"Edit_896b1353-43b5-4246-bd16-3d527eb2e4bc.bmp\")
. Kadri and Halat provided many examples and applications for such new mixed distributions. In this paper, we introduce a new mixed distribution of the Generalized Erlang distribution, which is derived from the Hypoexponential distribution. We characterize this new distribution by deriving simply closed expressions for the related functions of the probability density function, cumulative distribution function, moment generating function, reliability function, hazard function, and moments.
