An application of the new model is also illustrated using the three real data sets.
📌 3 Maddede Bu Makale
🎯
Amaç & Hipotez:In this paper, a new discrete distribution is introduced by compounding the geometric distribution with a zero truncated Poisson distribution, named geometric-zero truncated Poisson (GZTP) distribution.
📊
Temel Bulgular & Veri:Some basic properties of the new distribution, such as the hazard rate function, moments, mode, median, etc., are studied.
💡
Sonuç & Katkı:An application of the new model is also illustrated using the three real data sets.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri
Abstract
In this paper, a new discrete distribution is introduced by compounding the geometric distribution with a zero truncated Poisson distribution, named geometric-zero truncated Poisson (GZTP) distribution. Some basic properties of the new distribution, such as the hazard rate function, moments, mode, median, etc., are studied. We show mathematically and numerically that the hazard rate function is increasing. The model parameters are estimated by the moment, least squared error and maximum likelihood methods. A simulation study is performed to compare the performance of the different estimators in terms of bias and mean squared error. An application of the new model is also illustrated using the three real data sets.
🔖
Bu Makaleye Atıf Yap
BIDRAM, H., KUŞ, C., AKDOĞAN, Y., KINACI, İ. (2022). Geometric-Zero Truncated Poisson Distribution: Properties and Applications. Gazi University Journal of Science, Cilt: 32 - Sayı: 4, 1339–1354. https://ajindex.com/articles/521334
Adamidis, K., Loukas, S., "A lifetime distribution with decreasing failure rate", Statistics and Probability Letters, 39: 35-42, (1998)
Barreto-Souza, W., Morais, A.L., Cordeiro, G.M., "The Weibull-geometric distribution." Journal of Statistical Computation and Simulation, 81(5): 645-657, (2011)
Hemmati, F., Khorram, E., Rezakhah, S., "A new three-parameter ageing distribution", Journal of Statistical Planning and Inference, 141: 2266-2275, (2011)
Lu, W., Shi, D., "A new compounding life distribution: The Weibull-Poisson distribution." Journal of Applied Statistics, 39: 21-38, (2012)
Kuş, C., "A new lifetime distribution", Computational Statistics and Data Analysis, 51: 44974509, (2007)
Tahmasbi, R., Rezaei, S., "A two-parameter lifetime distribution with decreasing failure rate." Computational Statistics and Data Analysis, 52: 3889-3901, (2008)
Kemp, A.W., "Classes of discrete lifetime distributions", Communications in Statistics-Theory and Methods 33: 3069-3093, (2004)
Akdoğan, Y., Kuş, C., Asgharzadeh, A., Kınacı, I., Sharafi, F., "Uniform-geometric distribution." Journal of Statistical Computation and Simulation, 86(9): 1754-1770, (2016)
Gomez - Deniz, E., "A new discrete distribution: properties and applications in medical care", Journal of Applied Statistics, 40: 2760-2770, (2013)
Nakagawa, T., Zhao, X., "Optimization Problems of a Parallel System with a Random Number of Units", IEEE Transactions on Reliability, 61: 543-548, (2012)
Keilson, J., H. Gerber, H., "Some results for discrete unimodality." Journal of the American Statistical Association, 66: 386-389, (1971)
Braden, B., "Calculating sums of infinite series", The American Mathematical Monthly, 99(7): 649655, (1992)
Ferguson, T.S., A course in large sample theory, London: Chapman and Hall. (1996)
Nakagawa, T., Osaki, S., 1975. "The discrete Weibull distribution”, IEEE Transactions on Reliability, 24: 300-301, (1975)
Nekoukhou, V., H. Bidram, H., "The exponentiated discrete Weibull distribution", SORT, 39: 127146, (2015)
Nekoukhou, V., Alamatsaz, M.H., Bidram. H., "A discrete analogue of the generalized exponential distribution", Comm. Statist. Theory Methods, 41: 2000-2013, (2012)