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Open Access Research Article

Predicting a random determinant of order n filled with independently and identically distributed (i.i.d) exponential variates

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pp. 455–461Vol. 29Issue 5May 2026DOI: 10.47974/JSMS-1531XML
Received:
01 Apr 2025
Published Online:
16 Feb 2026
Article type:
Research Article
Language:
EN
Article no.:
JSMS-1531
Pages:
455–461

Abstract

The paper derives the fiducial limits for a determinant D of order 4, filled with independently and identically distributed (i.i.d) Exponential variates, using Chebyshev’s inequality and then, comparing the derived result with the fiducial limits for D of order 2 and 3 obtained in previous research, generalizes the result for order n. If D is of order n with i.i.d Exponential variates (θ), P(–k √(n+1)!)/θ2n  < D < k √(n+1)!)/θ2n ≥ (1 – 1/k2)  where k is a positive integer with E(D) = 0 and Var(D) = (n+1)!)/θ2n Several applications are pointed out. The study may be extended to other probability distributions.

Keywords

Subject Classifications

62P99

References

[1] S. C. Gupta and V. K. Kapoor, “Fundamental of Mathematical Statistics”, Sultan Chand and Sons (2014).
[2] T. Muir, “A Treatise on the theory of determinants”, Nabu Press (2011).
[3] G. L. Wise and E. B. Hall, “A note on the distribution of the determinant of a random matrix”. Statistics and Probability Letters, vol. 11, no. 2., pp. 147-148 (Feb 1991), https://doi.org/10.1016/0167-7152(91)90132-B.
[4] N. Saha and S. Chakraborty, “Probabilistic Analysis of a Random Determinant”, GRIN Verlag (2019).
[5] N. Saha and S. Chakraborty, “Using Chebyshev’s inequality to predict a Random Determinant for i.i.d Gamma and Weibull distributions”, Journal of Statistics and Management Systems, vol. 24, no. 3, pp. 613 – 623 (2021),  https://doi.org/10.1080/09720510.2020.1766766.

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