Some mathematical properties of Odd Kappa-G family

References

• Ahsanullah, M. (1995). Record statistics. Nova Science Publishers.
   Google Scholar
• Ahsanullah, M. (2004). record values–theory and applications. Record Values. University Press of America.
   Google Scholar
• Al-Hussaini, E. K., & Ahsanullah, M. (2015). Exponentiated distributions. Springer.
   Google Scholar
• Al-Shomrani, Ali A., & Shawky, A. I. (2016). Some characterization for record values. Acta Scientiae Et Intellectus, 20(1), 0 49–13. https://drive.google.com/file/d/1-WVA4g4Tz9XHHaR63ZLQ28XdP1CyqeIN/view
   Google Scholar
• Al-Shomrani, Ali A., Osama Arif, A. S., Hanif, S., Qaiser Shahbaz, M., & Shahbaz, M. Q. (2016). Topp–Leone family of distributions: Some properties and application. Pakistan Journal of Statistics and Operation Research, 120(3), 0 443–451. https://doi.org/10.18187/pjsor.v12i3.1458
   Google Scholar
• Al-Shomrani, Ali A. (2016a). Characterization and recurrence relations of certain distributions of kth upper record values. Advances and Applications in Statistics, 480(5), 0 349–361. https://doi.org/10.17654/AS048050349
   Google Scholar
• Al-Shomrani, Ali A. (2016b). Some characterization and relations based on k-th lower record values. The Open Statistics & Probability Journal, 70(1), 0 36–44. https://doi.org/10.2174/1876527001607010036
   Google Scholar
• Al-Shomrani, Ali A. (2018, August). New generalizations of extended beta and hypergeometric functions. Far East Journal of Theoretical Statistics, 540(4), 0 381–406. https://doi.org/10.17654/ts054040381
   Google Scholar
• Al-Shomrani, Ali A., & Al-Arfaj, A. (2021). A new flexible odd kappa-g family of distributions: Theory and properties. Advances and Applications in Mathematical Sciences, 210(1), 0 3443–3514. https://www.mililink.com/upload/article/245790492aams_vol_2012_october_2021_a43_p3443-3514_ali_a._al-shomrani,_ahmed_al-arfaj_read.pdf
   Google Scholar
• Albert, W. M., & Olkin, I. (1997 9). A new method for adding a parameter to a family of distributions with application to the exponential and weibull families. Biometrika, 840(3), 0 641–652. https://doi.org/10.1093/biomet/84.3.641
   Google Scholar
• Alexander, C., Cordeiro, G. M., Ortega, E. M. M., & María Sarabia, J. (2012). Generalized beta-generated distributions. Computational Statistics & Data Analysis, 560(6), 0 1880–1897. https://www.sciencedirect.com/science/article/pii/S0167947311004129
   Web of Science ®Google Scholar
• Aljarrah, M. A., Lee, C., & Famoye, F. (2014 June). On generating t-x family of distributions using quantile functions. Journal of Statistical Distributions and Applications, 10(1), 0 2. https://doi.org/10.1186/2195-5832-1-2
   Google Scholar
• Almetwally, E. M. Parameter estimation of bivariate models under some censoring schemes. (2019). LAP LAMBERT Academic Publishing. https://www.morebooks.de/store/gb/book/parameter-estimation-of-bivariate-models-under-some-censoring-schemes/isbn/978-620-0-47670-8
   Google Scholar
• Alzaatreh, A., Lee, C., & Famoye, F. (2013 June). A new method for generating families of continuous distributions. METRON, 710(1), 0 63–79. https://doi.org/10.1007/s40300-013-0007-y
   Google Scholar
• Alzaatreh, A., Lee, C., & Famoye, F. (2014 July). T-normal family of distributions: A new approach to generalize the normal distribution. Journal of Statistical Distributions and Applications, 10(1), 0 16. https://doi.org/10.1186/2195-5832-1-16
   Google Scholar
• Alzaghal, A., Famoye, F., & Lee, C. (2013). Exponentiated tx family of distributions with some applications. International Journal of Statistics and Probability, 20(3), 0 31. https://doi.org/10.5539/ijsp.v2n3p31
   Google Scholar
• Arnold, B. C., Balakrishnan, N., & Nagaraja, H. N. (2008). A first course in order statistics. In Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (pp. xviii + 273). https://epubs.siam.org/doi/book/10.1137/1.9780898719062
   Google Scholar
• Barry, C. A., Balakrishnan, N., & Nagaraja, H. N. (1998). Records. John Wiley & Sons. https://doi.org/10.1002/9781118150412
   Google Scholar
• Bourguignon, M., Silva, R. B., & Cordeiro, G. M. (2014). The weibull-g family of probability distributions. Journal of Data Science, 120(1), 0 53–68. https://www.jds-online.com/files/JDS-1210.pdf
   Google Scholar
• Chandler, K. N. (1952). The distribution and frequency of record values. Journal of the Royal Statistical Society. Series B (Methodological), 140(2), 0 220–228. http://www.jstor.org/stable/2983870
   Google Scholar
• Coles, S. (2001). An introduction to statistical modeling of extreme values (1 ed.). Springer. https://doi.org/10.1007/978-1-4471-3675-0
   Google Scholar
• Deheuvels, P. Paul Deheuvels. (1984). The characterization of distributions by order statistics and record values: A unified approach. Journal of Applied Probability, 210(2), 0 326–334. http://www.jstor.org/stable/3213643
   Google Scholar
• Dziubdziela, W., & Kopociński, B. (1976). Limiting properties of the k-th record values. Applicationes Mathematicae, 20(15), 0 187–190. https://doi.org/10.4064/am-15-2-187-190
   Google Scholar
• El-Sherpieny, E.-S. A., Muhammed, H. Z., & Almetwally, E. M. (2021 July). Bivariate weibull-g family based on copula function: Properties, Bayesian and non-Bayesian estimation and applications. Statistics, Optimization & Information Computing, 10(3), 678–709. http://www.iapress.org/index.php/soic/article/view/1129
   Google Scholar
• Eugene, N., Lee, C., & Famoye, F. (2002). Beta-normal distribution and its applications. Communications in Statistics - Theory and Methods, 310(4), 0 497–512. https://doi.org/10.1081/STA-120003130
   Web of Science ®Google Scholar
• Famoye, F., Lee, C., & Alzaatreh, A. (2013). Some recent developments in probability distributions. In Proceedings of the 59th world statistics congress, https://www.statistics.gov.hk/wsc/STS084-P3-S.pdf
   Google Scholar
• Farlie, D. J. G. (1960 12). The performance of some correlation coefficients for a general bivariate distribution. Biometrika, 470(3–4), 0 307–323. https://doi.org/10.1093/biomet/47.3–4.307
   Web of Science ®Google Scholar
• Franco, M., & Ruiz, J. M. (1996). On characterization of continuous distributions by conditional expectation of record values. Sankhyā: The Indian Journal of Statistics, Series A (1961-2002), 580(1), 0 135–141. http://www.jstor.org/stable/25051089
   Google Scholar
• Franco, M., & Jose, M. R. (1997 January). On characterizations of distributions by expected values of order statistics and record values with gap. Metrika, 450(1), 0 107–119. https://doi.org/10.1007/BF02717097
   Web of Science ®Google Scholar
• Galambos, J. (1987). The asymptotic theory of extreme order statistics. In Wiley series in probability and mathematical statistics. R.E. Krieger Publishing Company. https://www.worldcat.org/title/asymptotic-theory-of-extreme-order-statistics/oclc/13360715
   Google Scholar
• Gauss, M. C., & de Castro, M. (2011). A new family of generalized distributions. Journal of Statistical Computation and Simulation, 810(7), 0 883–898. https://doi.org/10.1080/00949650903530745
   Google Scholar
• Glänzel, W. (1987). A characterization theorem based on truncated moments and its application to some distribution families. 75–84. https://doi.org/10.1007/978-94-009-3965-3_8
   Google Scholar
• Glänzel, W. (1990). Some consequences of a characterization theorem based on truncated moments. Statistics, 210(4), 0 613–618. https://doi.org/10.1080/02331889008802273
   Google Scholar
• Glänzel, W., & Hamedani, G. G. (2001). Characterizations of nivariate continuous distributions. Studia Scientiarum Mathematicarum Hungarica, 370(1–2), 0 83–118. https://doi.org/10.1556/sscmath.37.2001.1–2.5
   Web of Science ®Google Scholar
• Gumbel, E. J. (1960). Bivariate exponential distributions. Journal of the American Statistical Association, 550(292), 0 698–707. https://www.tandfonline.com/doi/abs/10.1080/01621459.1960.10483368
   Google Scholar
• Gupta, R. C., Gupta, P. L., & Gupta, R. D. (1998). Modeling failure time data by Lehman alternatives. Communications in Statistics - Theory and Methods, 270(4), 0 887–904. https://doi.org/10.1080/03610929808832134
   Web of Science ®Google Scholar
• Haan, L., & Ferreira, A. (2006). Extreme value theory: An introduction (1 ed.). Springer. https://doi.org/10.1007/0-387-34471-3
   Google Scholar
• Hamedani, G. (2010). Characterizations of continuous univariate distributions based on the truncated moments of functions of order statistics. Studia Scientiarum Mathematicarum Hungarica, 470(4), 0 462–484. https://doi.org/10.1556/sscmath.2009.1143
   Web of Science ®Google Scholar
• Hamid Khan, A., Faizan, M., & Haque, Z. (2010). Characterization of continuous distributions through record statistics. Communications of the Korean Mathematical Society, 25(3), 0 485–489. https://doi.org/10.4134/CKMS.2010.25.3.485
   Google Scholar
• Hussain, S. (2015). Properties, extension and application of kappa distribution (M. Phil thesis). Government College University.
   Google Scholar
• Javed, M., Nawaz, T., & Irfan, M. (2019). The Marshall-Olkin kappa distribution: Properties and applications. Journal of King Saud University - Science, 310(4), 0 684–691. https://www.sciencedirect.com/science/article/pii/S101836471731323X
   Web of Science ®Google Scholar
• Jones, M. C. (2009). Kumaraswamyś distribution: A beta-type distribution with some tractability advantages. Statistical Methodology, 60(1), 0 70–81. https://www.sciencedirect.com/science/article/pii/S1572312708000282
   Google Scholar
• Jones, M. C. (2015). On families of distributions with shape parameters. International Statistical Review, 830(2), 0 175–192. https://onlinelibrary.wiley.com/doi/abs/10.1111/insr.12055
   Google Scholar
• Kotz, S., & Nadarajah, S. (2000). Extreme value distributions: Theory and applications. Imperial College Press. https://doi.org/10.1142/p191
   Google Scholar
• Leadbetter, M. R., Lindgren, G., & Rootzén, H. (2012). Extremes and related properties of random sequences and processes. Springer Science & Business Media.
   Google Scholar
• Lee, C., Famoye, F., & Alzaatreh, A. Y. (2013). Methods for generating families of univariate continuous distributions in the recent decades. WIREs Computational Statistics, 50(3), 0 219–238. https://wires.onlinelibrary.wiley.com/doi/abs/10.1002/wics.1255
   Google Scholar
• López Bláquez, F., & Luis Moreno Rebollo, J. (1997). A characterization of distributions based on linear regression of order statistics and record values. Sankhyā: The Indian Journal of Statistics, Series A (1961-2002), 590(3), 0 311–323. http://www.jstor.org/stable/25051162
   Google Scholar
• Mahdavi, A., & Kundu, D. (2017). A new method for generating distributions with an application to exponential distribution. Communications in Statistics - Theory and Methods, 460(13), 0 6543–6557. https://doi.org/10.1080/03610926.2015.1130839
   Web of Science ®Google Scholar
• Merovci, F., Alizadeh, M., & Hamedani, G. G. (2016 June). Another generalized transmuted family of distributions: Properties and applications. Austrian Journal of Statistics, 450(3), 0 71–93. https://www.ajs.or.at/index.php/ajs/article/view/doi
   Google Scholar
• Miroslav, M. R., & Balakrishnan, N. (2012). The gamma-exponentiated exponential distribution. Journal of Statistical Computation and Simulation, 820(8), 0 1191–1206. https://doi.org/10.1080/00949655.2011.574633
   Google Scholar
• Morgenstern, D. (1956). Einfache beispiele zweidimensionaler verteilungen. Mitteilingsblatt fur Mathematische Statistik, 8, 234–235. https://doi.org/10.1007/BF01897803; https://link.springer.com/article/10.1007/BF01897803
   Google Scholar
• Muhammad, H. T., & Gauss, M. C. (2016 October). Compounding of distributions: A survey and new generalized classes. Journal of Statistical Distributions and Applications, 30(1), 0 13. https://doi.org/10.1186/s40488-016-0052-1
   Google Scholar
• Nadarajah, S., & Kotz, S. (2006 June). The exponentiated type distributions. Acta Applicandae Mathematica, 920(2), 0 97–111. https://doi.org/10.1007/s10440-006-9055-0
   Web of Science ®Google Scholar
• Nagaraja, H. N. (1988a). Some characterizations of continuous distributions based on regressions of adjacent order statistics and record values. Sankhyā: The Indian Journal of Statistics, Series A (1961-2002), 500(1), 0 70–73. http://www.jstor.org/stable/25050681
   Google Scholar
• Nagaraja, H. N. (1988b). Record values and related statistics - A review. Communications in Statistics - Theory and Methods, 170(7), 0 2223–2238. https://doi.org/10.1080/03610928808829743
   Web of Science ®Google Scholar
• Nawaz, T., Hussain, S., Ahmad, T., Naz, F., & Abid, M. (2020). Kumaraswamy generalized kappa distribution with application to stream flow data. Journal of King Saud University - Science, 320(1), 0 172–182. https://www.sciencedirect.com/science/article/pii/S1018364718303902
   Web of Science ®Google Scholar
• Nevzorov, V. B. (2001). Records: Mathematical theory. Providence. translated from the russian manuscript by professor dmitry m. chibisov. Translations of Mathematical Monographs, 194. https://doi.org/10.1090/mmono/194
   Google Scholar
• Paul, W. M. (1973). Another family of distributions for describing and analyzing precipitation data. Journal of Applied Meteorology and Climatology, 120(2), 0 275–280. https://journals.ametsoc.org/view/journals/apme/12/2/1520-0450_1973_012_0275_afodfd_2_0_co_2.xml
   Google Scholar
• Paul, W. M., & Earl, S. J. (1973). Three-parameter kappa distribution maximum likelihood estimates and likelihood ratio tests. Monthly Weather Review, 1010(9), 0 701–707. https://journals.ametsoc.org/view/journals/mwre/101/9/1520-0493_1973_101_0701_tkdmle_2_3_co_2.xml
   Google Scholar
• Roger, B. N. (2006). An introduction to copulas (2nd ed.). Springer. https://doi.org/10.1007/0-387-28678-0
   Google Scholar
• Sidney, I. R. (1987). Extreme values, regular variation and point processes (1 ed.). Springer. https://doi.org/10.1007/978-0-387-75953-1
   Google Scholar
• Sklar, A. (1996). Random variables, distribution functions, and copulas: A personal look backward and forward. Lecture notes-monograph Series, 28, 1–14. https://doi.org/10.1214/lnms/1215452606
   Google Scholar
• Solomonovich Gradshteyn, I., & Moiseevich Ryzhik, I. (2007). Table of integrals, series, and products. Academic press.
   Google Scholar
• Sriboonchitta, S., & Kreinovich, V. (2018 May). Why are fgm copulas successful? A simple explanation. Advances in Fuzzy Systems, 2018, 0 1–5.https://doi.org/10.1155/2018/5872195; https://www.hindawi.com/journals/afs/2018/5872195/
   Web of Science ®Google Scholar
• Tahir, M. H., & Nadarajah, S. (2015). Parameter induction in continuous univariate distributions: Well-established g families. Anais da Academia Brasileira de Ciências, 870(2), 0 539–568. https://doi.org/10.1590/0001-3765201520140299
   Web of Science ®Google Scholar
• Torabi, H., & Montazeri Hedesh, N. (2012). The gamma-uniform distribution and its applications. Kybernetika, 480(1), 0 16–30. https://www.kybernetika.cz/content/2012/1/16
   Google Scholar
• Zografos, K., & Balakrishnan, N. (2009). On families of beta- and generalized gamma-generated distributions and associated inference. Statistical Methodology, 60(4), 0 344–362. https://www.sciencedirect.com/science/article/pii/S1572312708000841
   Google Scholar