On the Existence and Uniqueness of the Maximum Likelihood Estimators of Normal and Lognormal Population Parameters with Grouped Data

Table 6

Grouped data: 𝜏₁=−3.5, 𝜏₂=−0.5, 𝜏₃=2.5, 𝜏₄=5.5, 𝜏₅=8.5.

S.S	𝑚			𝜈
𝑛	Average	A.W.	C.R.	Average	A.W.	C.R.
30	21.641	32.122	90.8%	170.705	505.267	77.8%
35	21.386	30.498	92.8%	167.457	517.091	80.3%
40	21.250	28.960	93.5%	164.214	555.646	83.9%
50	21.035	26.623	95.2%	161.572	583.249	88.7%
100	20.469	17.481	94.1%	154.492	271.900	88.7%