Expectation properties of generalized order statistics based on the Gompertz-G family of distributions

• Autorzy: Alharbi Yousef F. , Fawzy Mohamad A. , Athar Haseeb

Identyfikatory

DOI

10.37190/ord230401

• Języki publikacji: EN

Abstrakty

EN

Gompertz-G family of distributions has been considered. The moment properties of generalized order statistics were studied and characterization results have been presented. Further, several examples and special cases were discussed. The results can be applied to many known distributions included in this family.

Słowa kluczowe

EN

generalized order statistics; expectation identities; Gompertz-G family of distributions; characterization

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Operations Research and Decisions
• Rocznik: 2023
• Tom: Vol. 33, No. 4
• Strony: 1--14
• Opis fizyczny: Bibliogr. 32 poz.

Twórcy

autor

Alharbi Yousef F.

• Department of Mathematics, College of Science, Taibah University, Al Madinah, Kingdom of Saudi Arabia

autor

Fawzy Mohamad A.

• Department of Mathematics, College of Science, Taibah University, Al Madinah, Kingdom of Saudi Arabia
• Mathematics Department, Faculty of Science, Suez University, Suez, Egypt

autor

Athar Haseeb

• Department of Statistics and Operations Research, Faculty of Science, Aligarh Muslim University, India

Bibliografia

• [1] Ahmad, A. E.-B. A., and Fawzy, M. A. Recurrence relations for single moments of generalized order statistics from doubly truncated distributions. Journal of Statistical Planning and Inference 117, 2 (2003), 241–249.
• [2] Ahsanullah, M. Record Statistics. Nova Science Publishers, New York, 1995.
• [3] Al Hussaini, E. K., Ahmad, A. E.-B. A., and Al Kashif, M. A. Recurrence relations for moment and conditional moment generating functions of generalized order statistics. Metrika 61, 2 (2005), 199–220.
• [4] Alizadeh, M., Cordeiro, G. M., Bastos Pinho, L. G., and Ghosh, I. The Gompertz-G family of distribution. Journal of Statistical Theory and Practice 11, 1 (2017), 179–207.
• [5] Anwar, Z., Athar, H., and Khan, R. U. Expectation identities based on recurrence relations of functions of generalized order statistics. Journal of Statistical Research 41, 2 (2007), 93–102.
• [6] Arnold, B. C., Balakrishnan, N., and Nagaraja, H. N. Records. John Wiley and Sons, New York, 1998.
• [7] Athar, H., and Islam, H. M.-U. Recurrence relations between single and product moments of generalized order statistics from a general class of distributions. Metron - International Journal of Statistics, 62, 3 (2004), 327–337.
• [8] Athar, H., and Nayabuddin. Expectation identities of generalized order statistics from Marshall-Olkin extended uniform distribution and its characterization. Journal of Statistical Theory and Applications 14, 2 (2015), 184–191.
• [9] Athar, H., Nayabuddin, and Khwaja, S. K. Expectation identities of Pareto distribution based on generalized order statistics and its characterization. American Journal of Applied Mathematics and Mathematical Sciences 1, 1 (2012), 23–29.
• [10] Athar, H., Nayabuddin, and Zarrin, S. Generalized order statistics from Marshall-Olkin extended exponential distribution. Journal of Statistical Theory and Applications 18, 2 (2019), 129–135.
• [11] Athar, H., Noor, Z., Zarrin, S., and Al Mutairi, H. N. S. Expectation properties of generalized order statistics from Poisson Lomax distribution. Statistics, Optimization & Information Computing 9, 3 (2021), 735–747.
• [12] Athar, H., Zarrin, S., and Noor, Z. Moment properties of generalized order statistics from Weibull-Geometric distribution. Applied Mathematics E-Notes 19 (2019), 199–209.
• [13] Balakrishnan, N., and Aggarwala, R. Progressive Censoring. Theory, Methods, and Applications. Birkhauser, Boston, 2000.
• [14] Bodhisuwan, W., and Aryuyuen, S. The Gompertz Weibull Frechet distribution: Properties and applications. Thailand Statistician 19, 4 (2021), 659–676.
• [15] Cramer, E., and Kamps, U. Relations for expectations of functions of generalized order statistics. Journal of Statistical Planning and Inference 89, 1-2 (2000), 79–89.
• [16] David, H. A., and Nagaraja, H. N. Order Statistics. John Wiley and Sons, New York, 2003.
• [17] Eghwerido, J. T., Zelibe, S. C., and Efe-Eyefia, E. Gompertz-alpha power inverted exponential distribution: Properties and applications. Thailand Statistician 18, 3 (2020), 319–332.
• [18] Hwang, J. S., and Lin, G. D. Extensions of Muntz-Szasz theorems and application. Analysis 4, 1-2 (1984), 143–160.
• [19] Kamps, U. A concept of generalized order statistics. Journal of Statistical Planning and Inference 48, 1 (1995), 1–23.
• [20] Kamps, U., and Cramer, E. On distributions of generalized order statistics. Statistics 35, 3 (2001), 269–280.
• [21] Keseling, C. Conditional distributions of generalized order statistics and some characterizations. Metrika 49, 1 (1999), 27–40.
• [22] Khan, R. U., and Khan, M. A. Moment properties of generalized order statistics from exponential-Weibull lifetime distribution. Journal of Advanced Statistics 1, 3 (2016), 146–155.
• [23] Khan, R. U., Kumar, D., and Athar, H. Moments of generalized order statistics from Erlang-truncated exponential distribution and its characterization. International Journal of Statistics and Systems 5, 4 (2010), 455–464.
• [24] Khan, R. U., and Zia, B. Generalized order statistics of doubly truncated linear exponential distribution and a characterization. Journal of Applied Probability and Statistics 9, 1 (2014), 53–65.
• [25] Khwaja, S. K., Athar, H., and Nayabuddin. Lower generalized order statistics from extended type I generalized logistic distribution. Journal of Applied Statistical Science 20, 1 (2012), 21–28.
• [26] Nayabuddin, and Athar, H. Recurrence relations for single and product moments of generalized order statistics from MarshallOlkin extended Pareto distribution. Communications in Statistics - Theory and Methods 46, 16 (2017), 7820–7826.
• [27] Oguntunde, P. E., Khaleel, M. A., Adejumo, A. O., Okagbue, H. I., Opanuga, A. A., and Owolabi, F. O. The Gompertz inverse exponential (GoIE) distribution with applications. Cogent Mathematics & Statistics 5, 1 (2018), 1507122.
• [28] Oguntunde, P. E., Khaleel, M. A., Ahmed, M. T., and Okagbue, H. I. The Gompertz Frechet distribution: properties and applications. Cogent Mathematics & Statistics 6, 1 (2019), 1568662.
• [29] Pawlas, P., and Szynal, D. Recurrence relations for single and product moments of generalized order statistics from Pareto, generalized Pareto and Burr distributions. Communications in Statistics - Theory and Methods 30, 4 (2001), 739–746.
• [30] Saran, J., and Pandey, A. Recurrence relations for marginal and joint moment generating functions of generalized order statistics from power function distribution. Metron - International Journal of Statistics 61, 1 (2003), 27–33.
• [31] Singh, B., Khan, R. U., and Khan, M. A. R. Generalized order statistics from Kumaraswamy-Burr III distribution and related inference. Journal of Statistics: Advances in Theory and Applications 19, 1 (2018), 1–16.
• [32] Zarrin, S., Athar, H., and Abdel-Aty, Y. Relations for moments of generalized order statistics from power Lomax distribution. Journal of Statistics Applications & Probability Letters 6, 1 (2019), 29–36.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).