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On the tail integral formulae for real-valued random variables

Published online by Cambridge University Press:  12 October 2022

Saralees Nadarajah  and
Idika E. Okorie
Saralees Nadarajah
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL e-mail: mbbsssn2@manchester.ac.uk
Idika E. Okorie
Affiliation:
Department of Mathematics, Khalifa University, P.O. Box 127788, Abu Dhabi, UAE email: idika.okorie@ku.ac.ae
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Extract

The most important properties of any distribution are its moments. The first four moments, for example, can be used describe any data set fairly well. Moments can also be used for estimation.

Type
Articles
Information
The Mathematical Gazette , Volume 106 , Issue 567 , November 2022 , pp. 487 - 493
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Copyright
© The Authors, 2022. Published by Cambridge University Press on behalf of The Mathematical Association

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References

Nadarajah, S. and Mitov, K., Product moments of multivariate random vectors, Communications in statistics − theory and methods 32 (2003) pp. 47-60.Google Scholar
Hong, L., A remark on the alternative expectation formula, The American Statistician 66 (2012) pp. 232–233.Google Scholar
Hong, L., Another remark on the alternative expectation formula, The American Statistician 69 (2015) pp. 157–159.Google Scholar
Chakraborti, S., Jardim, F. and Epprecht, E., (2018), Higher order moments using the survival function: the alternative expectation, The American Statistician 73 (2019) pp. 191–194.Google Scholar
Hoeffding, W., Korrelationtheorie, Masstabinvariante, Schriften Math. Inst. Univ. Berlin 5 (1940) pp. 181–233.Google Scholar
Mardia, K. V., Some contributions to contingency-type bivariate distributions, Biometrika 54 (1967) pp. 235–249.Google ScholarPubMed
Block, H. W. and Fang, Z., A multivariate extension of Hoeffding’s lemma, Annals of Probability 16 (1988) pp. 1803–1820.Google Scholar
Lo, A., Demystifying the integrated tail probability expectation formula, The American Statistician 73 (2019) pp. 367–374.Google Scholar
Berkowitz, J., Testing density forecasts, with applications to risk management, Journal of Business and Economic Statistics 19 (2001) pp. 465-474.Google Scholar
Kim, J. H. T., Conditional tail moments of the exponential family and its related distributions, North American Actuarial Journal 14 (2010) pp. 198–216.Google Scholar
Zambrano, J. A., Higher-order tail moments in asset-pricing theory in Handbook of global financial markets, World Scientific (2017).Google Scholar
Hoga, Y., Extreme conditional tail moment estimation under serial dependence, Journal of Financial Econometrics 17 (2019) pp. 587–615.Google Scholar
https://en.m.wikipedia.org/wiki/Weibull_distribution#Shannon_entropy Google Scholar
Sarabia, J. M., Gomez-Deniz, E., Prieto, F. and Jorda, V., Risk aggregation in multivariate dependent Pareto distributions, Insurance: Mathematics and Economics 71 (2016) pp. 154–163.Google Scholar
Cuadras, C. M., On the covariance between functions, Journal of Multivariate Analysis 81 (2002) pp. 19–27.Google Scholar
Lo, A., Functional generalizations of Hoeffding’s covariance lemma and a formula for Kendall’s tau, Statistics and Probability Letters 122 (2017) pp. 218–226.Google Scholar