An Improved Laguerre-Samuelson Inequality of Chebyshev-Markov Type

Table 2

Simulation of completely symmetric sequences.

Normally distributed sequence
			Bound (20)
	0.56186	2.93964	3.95167	3.74642	9.94987
	−0.25589	3.43710	6.46976	6.68489	31.60696
	−0.02554	3.27371	11.85401	11.89163	99.995
	0.00311	4.54175	21.15554	21.14735	316.22618
	0.00119	5.19235	37.61159	37.60602	999.9995
Symmetrized gamma distributed sequence
			Bound (20)
	3.21672	3.75302	4.59915	4.71922	9.94987
	5.20859	5.71697	9.07142	8.40728	31.60696
	2.62489	5.97893	14.61965	14.95319	99.995
	2.92086	7.16258	26.45799	26.59143	316.22618
	2.90432	8.36365	47.04378	47.28707	999.9995
Cauchy distributed sequence
			Bound (20)	n. a.
	8.05412	4.62977	5.26901		9.94987
	495.87198	22.34806	22.35226		31.60696
	1948.05208	54.49966	59.56377		99.995
	47796.85784	221.09459	221.92773		316.22618
	346611.18426	644.25589	663.63445		999.9995