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Short Technical Notes

On Moments of Folded and Truncated Multivariate Normal Distributions

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Pages 930-934 | Received 01 Jun 2016, Published online: 09 Oct 2017

References

  • Arismendi, J. C. (2013), “Multivariate Truncated Moments,” Journal of Multivariate Analysis, 117, 41–75.
  • Berkane, M., and Bentler, P. M. (1986), “Moments of Elliptically Distributed Random Variates,” Statistics & Probability Letters, 4, 333–335.
  • Birnbaum, Z., and Meyer, P. L. (1953), “On the Effect of Truncation in Some or All Coordinates of a Multinormal Population,” Journal of the Indian Society of Agricultural Statistics, 5, 18–28.
  • Chakraborty, A. K., and Chatterjee, M. (2013), “On Multivariate Folded Normal Distribution,” Sankhyā, Series B, 75, 1–15.
  • Cohen, A. C. (1951a), “On Estimating the Mean and Variance of Singly Truncated Normal Frequency Distributions from the First Three Sample Moments,” Annals of the Institute of Statistical Mathematics, 3, 37–44.
  • ——— (1951b), “Estimation of Parameters in Truncated Pearson Frequency Distributions,” Annals of Mathematical Statistics, 22, 256–265.
  • ——— (1991), Truncated and Censored Samples: Theory and Applications, New York: Marcel Dekker.
  • Dyer, D. D. (1973), “On Moments Estimation of the Parameters of a Truncated Bivariate Normal Distribution,” Journal of the Royal Statistical Society, Series C, 22, 287–291.
  • Elandt, R. C. (1961), “The Folded Normal Distribution: Two Methods of Estimating Parameters from Moments,” Technometrics, 3, 551–562.
  • Fisher, R. A. (1931), “Properties and Applications of Hh Functions,” Introduction to British A.A.S. Mathematical Tables, 1, 26–35.
  • Gupta, A. K., and Tracy, D. S. (1976), “Recurrence Relations for the Moments of Truncated Multinormal Distribution,” Communications in Statistics—Theory and Methods, 5, 855–865.
  • Kamat, A. R. (1953), “Incomplete and Absolute Moments of the Multivariate Normal Distribution with Some Applications,” Biometrika, 40, 20–34.
  • Khatri, C. G., and Jaiswal, M. C. (1963), “Estimation of Parameters of a Truncated Bivariate Normal Distribution,” Journal of the American Statistical Association, 58, 519–526.
  • Lee, L. F. (1983), “The Determination of Moments of the Doubly Truncated Multivariate Normal Tobit Model,” Economics Letters, 11, 245–250.
  • Leone, F. C., Nelson, L. S., and Nottingham, R. B. (1961), “The Folded Normal Distribution,” Technometrics, 3, 543–550.
  • Maruyama, Y., and Seo, T. (2003), “Estimation of Moment Parameter in Elliptical Distributions,” Journal of the Japan Statistical Society, 33, 215–229.
  • Murthy, G. S. R. (2015), “A Note on Multivariate Folded Normal Distribution,” Sankhyā, Series B, 77, 108–113.
  • Nabeya, S. (1951), “Absolute Moments in 2-Dimensional Normal Distribution,” Annals of the Institute of Statistical Mathematics, 3, 2–6.
  • ——— (1952), “Absolute Moments in 3-Dimensional Normal Distribution,” Annals of the Institute of Statistical Mathematics, 4, 15–30.
  • ——— (1961), “Absolute and Incomplete Moments of the Multivariate Normal Distribution,” Biometrika, 48, 77–84.
  • Psarakis, S., and Panaretos, J. (2001), “On Some Bivariate Extensions of the Folded Normal and the Folded t Distributions,” Journal of Applied Statistical Science, 10, 119–136.
  • Rosenbaum, S. (1961), “Moments of a Truncated Bivariate Normal Distribution,” Journal of the Royal Statistical Society, Series B, 23, 405–408.
  • Shah, S. M., and Parikh, N. T. (1964), “Moments of Single and Doubly Truncated Standard Bivariate Normal Distribution,” Vidya, 7, 82–91.
  • Takemura, A., and Takeuchi, K. (1988), “Some Results on Univariate and Multivariate Cornish-Fisher Expansion: Algebraic Properties and Validity,” Sankhyā, Series A, 50, 111–136.
  • Tallis, G. M. (1961), “The Moment Generating Function of the Truncated Multi-Normal Distribution,” Journal of the Royal Statistical Society, Series B, 23, 223–229.
  • Willink, R. (2005), “Normal Moments and Hermite Polynomials,” Statistics & Probability Letters, 73, 271–275.

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