Some results on uncorrelated dependent random variables

[1] C. Amblard and S. Girard, Symmetry and dependence properties within a semiparametric family of bivariate copulas, Journal of Nonparametric Statistics, 14, (2002), 715-727.

[2] M. Amini, H.R Nili Sani and A. Bozorgnia, Aspects of negative dependence structures, Communications in Statistics-Theory and Methods, 42, (2013), 907-917.

[3] H. Bazargan, H. Bahai, and A. Aminzadeh-Gohari, Calculating the return value using a mathematical model of signi cant wave height, Journal of Marine Science and Technology, 12, (2007), 34-42.

[4] B. Beckers, H. Herwartz, and M. Seidel, Risk forecasting in TGARCH models with uncorrelated dependent innovations, Quantitative Finance, 17(1), (2017), 121-137.

[5] J. Behboodian, Uncorrelated dependent random variables, Mathematics Magazine, 51(5), (1978), 303-304.

[6] J. Behboodian, Examples of uncorrelated dependent random variables using a bivariate mixture, The American Statistician, 44(3), (1990), 218.

[7] J. Behboodian, A. Dolati and M. Ubeda-Flores, Measures of association based on average quadrant dependence, Journal of Probability and Statistics, 3, (2005), 161-173.

[8] J. D. Brott, Zero correlation, independence and normality, The American Statistician, 40(4), (1986), 276-277.

[9] H. A. David, A historical note on zero correlation and independence, The American Statistician, 63(2), (2009), 185-186.

[10] L. Y. Deng and R.S. Chhikara, On the characterization of the exponential distribution by the independence of its integer and fractional parts, Statistica Neerlandica, 44(2), (1990), 83-85.

[11] T. M. Durairajan, A classroom note on sub-independence, Gujrat Statistical Research, 6, (1979), 17-18.

[12] N. Ebrahimi, G. G. Hamedani E. S Soo  and H. Volkmer, A class of models for uncor-related random variables, Journal of Multivariate Analysis, 101(8), (2010), 1859-1871.

[13] C. Francq, R. Roy, and J. M. Zakoan, Diagnostic checking in ARMA models with uncorrelated errors, Journal of the American Statistical Association, 100(470), (2005), 532-544.

[14] C. Francq and H. Rassi, Multivariate portmanteau test for autoregressive models with uncorrelated but nonindependent errors, Journal of Time Series Analysis, 28(3), (2007), 454-470.

[15] C. Genest, B. Remillard and D. Beaudoin, Goodness-of- t tests for copulas: A review and a power study, Insurance: Mathematics and economics, 44(2), (2009), 199-213.

[16] J. D. Gibbons, Mutually exclusive events, independence and zero correlation, The American Statistician, 22, (1968), 31-32.

[17] A. K. Gupta, D. Song, and G. Szekely, The dependence of uncorrelated statistics, Applied Mathematics Letters, 7(5), (1994), 29-32.

[18] G. G. Hamedani, H. Volkmer, and J. Behboodian, A note on sub-independent random variables and a class of bivariate mixtures, Studia Scientiarum Mathematicarum Hungarica, 49(1), (2012), 19-25.

[19] G. G. Hamedani, Sub-independence: An expository perspective, Communications in Statistics-Theory and Methods, 42(20), (2013), 3615-3638.

[20] G. G. Hamedani M. Maadooliat, Sub-Independence: A Useful Concept. Nova Science Publishers, 2015.

[21] K. Joag-Dev, Independence via uncorrelatedness under certain dependence structures, The Annals of Probability, 11, (1983), 1037-1041.

[22] H. Joe, Dependence Modeling with Copulas. CRC press, 2014.

[23] C. J. Kowalski, Non-normal bivariate distributions with normal marginals, The American Statistician, 27(3), (1973), 103-106.

[24] A. Krajka and D. Szynal, On measuring the dependence of uncorrelated random variables, Journal of Mathematical Sciences, 76(2), (1995), 2269-2274.

[25] H. O. Lancaster, Zero correlation and independence, Australian Journal of Statistics, 21, (1959), 53-56.

[26] T. H. Lee and X. Long, Copula-based multivariate GARCH model with uncorrelated dependent errors, Journal of Econometrics, 150(2), (2009), 207-218.

[27] I. N. Lobato, Testing that a dependent process is uncorrelated, Journal of the American Statistical Association, 96(455), (2001), 1066-1076.

[28] E. Lukacs, A characterization of the gamma distribution, Ann. Math. Statist., 26, (1955), 319{324.

[29] Y. B. Manassara, Multivariate portmanteau test for structural VARMA models with uncorrelated but non-independent error terms, Journal of Statistical Planning and Inference, 141(8), (2011), 2961-2975.

[30] Y. B. Manassara and H. Rassi, Semi-strong linearity testing in linear models with dependent but uncorrelated errors, Statistics and Probability Letters, 103, (2015), 110-115.

[31] G. Marsaglia, Random variables with independent integer and fractional parts, Statistica Neerlandica, 49(2), (1995), 133-137.

[32] P. Mikusinski, H. Sherwood, and M. D. Taylor, Shues of min, Stochastica, 13, (1992), 61{74.

[33] T. F. Mori and G. J. Szekely, Representations by uncorrelated random variables, Mathematical Methods of Statistics, 26(2), (2017), 149-153.

[34] R. B. Nelsen, An Introduction to Copulas. Springer Science & Business Media, 2007.

[35] E. Pollak, A comment on zero correlation and independence, The American Statistician, (1971), 25, 53.

[36] M. Scarsini, On measures of concordance, Stochastica, 8, (1984), 201{218.

[37] S. M. Schennach, Convolution without independence, Journal of Econometrics, 211(1), (2019), 308-318.

[38] B. Schweizer E. F. Wol , On nonparametric measures of dependence for random variables, Annals of Statistics, 9, (1981), 879-885.

[39] W. Shih, More on zero correlation and independence, The American Statistician, (1971), 25, 62.

[40] T. Shimura, Limit distribution of a roundo  error, Statistics and Probability Letters, 82(4), (2012), 713-719.

[41] A. Sklar, Fonctions de repartition a n dimensions et leurs marges, Publications de l'Institut de statistique de l'Universite de Paris, 8, (1959), 229-231.

[42] F. W. Steutel and J. G. F Thiemann, On the independence of integer and fractional parts, Statistica Neerlandica, 43(1), (1989), 53-59.

[43] V. Yeremieiev, Forecasting of the number of bird collisions with turbines in the territory of Pre-Azov region wind park using the route census method, Proceedings of E3S Web of Conferences Vol. 280, (EDP Sciences, 2021), p. 06010.