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Doubly noncentral singular matrix variate beta distributions. (English) Zbl 05902625

Summary: Using Greenacre’s definition of the symmetrised density function, in this paper, we propose an alternative approach to find the corresponding nonsymmetrised density function of doubly noncentral singular matrix variate beta type I and II distributions. As particular cases we obtain the noncentral singular matrix variate beta type I and II distributions.

MSC:

62-XX Statistics

References:

[1] Cadet A., Sankhyā A 58 pp 101– (1996)
[2] Chikuse Y., Multivariate Statistical Analysis pp 53– (1980)
[3] DOI: 10.1214/aos/1176345405 · Zbl 0496.62048 · doi:10.1214/aos/1176345405
[4] DOI: 10.1007/BF02482504 · Zbl 0588.62074 · doi:10.1007/BF02482504
[5] DOI: 10.1214/aoms/1177703863 · Zbl 0123.36801 · doi:10.1214/aoms/1177703863
[6] Chikuse Y., Ann. Inst. Statist. Math. Part A. 31 pp 465– (1979) · Zbl 0463.62045 · doi:10.1007/BF02480302
[7] Davis A. W., Multivariate Analysis V pp 287– (1980)
[8] Díaz-García J. A., Generalisations of some properties of invariant polynomials with matrix arguments (2006)
[9] Díaz-García J. A., J. Multivariate Anal. 93 (2) pp 196– (2005)
[10] Díaz-García J. A., J. Multivariate Anal. 94 (1) pp 109– (2005) · Zbl 1065.62096 · doi:10.1016/j.jmva.2004.08.003
[11] DOI: 10.1006/jmva.1997.1689 · Zbl 0886.62059 · doi:10.1006/jmva.1997.1689
[12] Díaz-Garcí J. A., Ann. Statist. 25 pp 2018– (1997) · Zbl 0881.62058 · doi:10.1214/aos/1069362383
[13] Díaz-García J. A., J. Statist. Research Iran 3 pp 191– (2006)
[14] Díaz-García J. A., Brazilian J. Prob. Statist. 21 pp 175– (2007)
[15] DOI: 10.1016/j.jmva.2007.02.006 · Zbl 1333.62049 · doi:10.1016/j.jmva.2007.02.006
[16] Farrell R. H., Multivariate Calculation: Use of the Continous Groups (1985) · doi:10.1007/978-1-4613-8528-8
[17] Goodall C. R., Ann. Statist. 7 pp 95– (1993)
[18] Gupta A. K., Matrix variate distributions (2000) · Zbl 0935.62064
[19] DOI: 10.1214/aoms/1177703550 · Zbl 0121.36605 · doi:10.1214/aoms/1177703550
[20] Khatri C. G., Sankhyā A 32 pp 311– (1970)
[21] DOI: 10.1214/aoms/1177705144 · Zbl 0101.13005 · doi:10.1214/aoms/1177705144
[22] DOI: 10.1002/9780470316559 · doi:10.1002/9780470316559
[23] DOI: 10.1214/aoms/1177703748 · Zbl 0128.14002 · doi:10.1214/aoms/1177703748
[24] Srivastava S. M., An Introduction to Multivariate Statistics (1979) · Zbl 0421.62034
[25] Srivastava S. M., Ann. Math. Statist. 39 pp 227– (1968) · Zbl 0174.22905 · doi:10.1214/aoms/1177698522
[26] Roux J. J.J., A modern course on tatistical distributions in scientific work. Model and structures pp 281– (1975) · doi:10.1007/978-94-010-1842-5_22
[27] DOI: 10.1214/aos/1176325375 · Zbl 0795.62052 · doi:10.1214/aos/1176325375
[28] Wilks S. S., Biometrika 24 pp 471– (1932) · Zbl 0006.02301 · doi:10.1093/biomet/24.3-4.471
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