Table 2.

Some specimen distributions to illustrate the impact of varying CV on the relative efficiency. Each distribution has mean 1 and is fully specified once the CV is given. The final column shows the greatest value of the CV² for which the distribution is available (given that z _i ≥ 0 necessarily). The Least Favorable Distribution minimizes Ψ(α) for all α≥ 0 over all such distributions with nonnegative support

	Support	Probabilities	Range	CV2	Max CV2
Three‐point symmetrical distributions
(b) Uniform (p = ⅓)	{a, 1, 2 – a}	{p, 1 – 2p, p}	2(1 – a)	2p(1 – a)2	0.6667
(c) Unimodal (p = ¼)					0.5000
(d) Bimodal (p = 2 / 5)					0.8000
Three‐point skew distributions
(e) Positive skew	{1 −S/3, 1 + S/6, 1 + 2S/3}	{½, ⅓, 1 / 6}	S	5S2/36	1.2500
(f) Negative skew	{1 −2S/3, 1 −S/6, 1 + S/3}	{1 / 6, ⅓, ½}	S	5S2/36	0.3125
Least Favorable Distribution (LFD)	{0, 1 + c 2}	$\left\{\frac{c^2}{1+c^2},\frac{1}{1+c^2}\right\}$	1 + c 2	c 2	∞