Table 1.

Coverage probabilities and (expected widths) of 95% CIs for the mean.

	Wald	M-Wald	Likelihood	Score	Wald	M-Wald	Likelihood	Score
$\mu =3$
n	$\theta =.5$				$\theta =1$
10	–	–	–	–	.872(3.92)	.918(5.00)	.871(3.99)	.873(5.04)
20	.882(3.75)	.901(4.17)	.923(7.87)	.890(3.92)	.896(2.90)	.920(3.22)	.902(2.95)	.933(3.77)
30	.899(3.12)	.915(3.34)	.937(4.54)	.909(3.24)	.920(2.40)	.934(2.57)	.923(2.43)	.938(2.81)
40	.910(2.74)	.920(2.88)	.941(3.53)	.918(2.81)	.926(2.09)	.938(2.20)	.931(2.11)	.940(2.35)
50	.915(2.46)	.922(2.56)	.942(3.00)	.921(2.51)	.928(1.88)	.936(1.96)	.933(1.90)	.945(2.06)
60	.919(2.25)	.926(2.33)	.943(2.65)	.926(2.30)	.930(1.72)	.937(1.78)	.933(1.73)	.945(1.86)
70	.925(2.09)	.931(2.15)	.949(2.40)	.929(2.13)	.935(1.60)	.940(1.64)	.938(1.61)	.947(1.70)
80	.928(1.96)	.933(2.01)	.946(2.21)	.933(1.99)	.936(1.50)	.940(1.53)	.938(1.50)	.948(1.58)
90	.929(1.85)	.933(1.89)	.948(2.05)	.934(1.88)	.937(1.41)	.943(1.44)	.940(1.42)	.949(1.48)
n	$\theta =4$				$\theta =10$
10	.943(2.95)	.975(3.76)	.940(3.44)	.932(2.88)	.961(2.71)	.986(3.45)	.952(2.62)	.952(2.90)
20	.938(2.02)	.958(2.24)	.938(2.12)	.936(1.99)	.950(1.82)	.972(2.03)	.946(1.79)	.955(1.86)
30	.935(1.63)	.950(1.75)	.938(1.68)	.941(1.62)	.956(1.46)	.969(1.56)	.953(1.44)	.953(1.47)
40	.941(1.41)	.951(1.48)	.941(1.44)	.938(1.40)	.949(1.25)	.960(1.32)	.947(1.24)	.947(1.26)
50	.940(1.26)	.950(1.31)	.942(1.28)	.938(1.25)	.951(1.11)	.958(1.16)	.948(1.10)	.949(1.11)
60	.946(1.15)	.952(1.19)	.947(1.17)	.944(1.15)	.950(1.01)	.957(1.04)	.947(1.00)	.950(1.01)
70	.943(1.06)	.950(1.09)	.945(1.07)	.943(1.06)	.948(0.93)	.955(0.96)	.947(0.93)	.950(0.93)
80	.946(0.99)	.952(1.02)	.948(1.01)	.946(0.99)	.945(0.87)	.951(0.89)	.945(0.86)	.947(0.87)
90	.947(0.94)	.952(0.96)	.947(0.95)	.946(0.94)	.949(0.82)	.954(0.83)	.948(0.81)	.950(0.82)
$\mu =5$
n	$\theta =.5$				$\theta =1$
10	–	–	–	–	.878(6.30)	.922(8.03)	.877(6.37)	.891(14.4)
20	.883(6.09)	.904(6.77)	.923(10.6)	.892(6.33)	.905(4.55)	.925(5.07)	.910(4.63)	.930(5.89)
30	.898(5.04)	.915(5.40)	.940(7.25)	.910(5.21)	.917(3.82)	.934(4.09)	.920(3.86)	.938(4.45)
40	.907(4.42)	.916(4.65)	.938(5.68)	.915(4.54)	.925(3.31)	.935(3.48)	.929(3.34)	.941(3.71)
50	.915(3.98)	.924(4.14)	.942(4.85)	.922(4.07)	.932(2.98)	.942(3.10)	.935(3.01)	.941(3.25)
60	.918(3.66)	.926(3.78)	.950(4.30)	.928(3.73)	.931(2.73)	.940(2.82)	.937(2.75)	.944(2.93)
70	.925(3.41)	.930(3.51)	.945(3.88)	.929(3.46)	.940(2.53)	.946(2.61)	.942(2.55)	.945(2.70)
80	.929(3.18)	.933(3.26)	.941(3.58)	.933(3.23)	.940(2.37)	.945(2.43)	.941(2.39)	.944(2.50)
90	.932(3.01)	.936(3.07)	.943(3.34)	.935(3.04)	.940(2.23)	.945(2.28)	.942(2.24)	.948(2.35)
n	$\theta =4$				$\theta =10$
10	.927(4.16)	.969(5.31)	.923(4.59)	.920(4.05)	.946(3.63)	.983(4.62)	.938(3.49)	.943(3.76)
20	.932(2.89)	.954(3.22)	.936(3.02)	.929(2.85)	.953(2.47)	.972(2.75)	.949(2.42)	.950(2.48)
30	.934(2.37)	.951(2.54)	.939(2.43)	.932(2.35)	.943(1.98)	.956(2.12)	.940(1.96)	.945(1.99)
40	.936(2.05)	.947(2.16)	.939(2.10)	.934(2.04)	.950(1.70)	.961(1.79)	.949(1.69)	.943(1.71)
50	.939(1.84)	.947(1.92)	.945(1.86)	.938(1.83)	.949(1.52)	.958(1.58)	.947(1.51)	.948(1.52)
60	.942(1.68)	.950(1.74)	.941(1.70)	.941(1.67)	.947(1.38)	.954(1.43)	.945(1.37)	.946(1.39)
70	.943(1.56)	.949(1.60)	.943(1.58)	.941(1.55)	.946(1.28)	.952(1.31)	.943(1.27)	.944(1.28)
80	.942(1.46)	.947(1.50)	.945(1.47)	.942(1.45)	.942(1.19)	.949(1.22)	.941(1.19)	.944(1.19)
90	.941(1.38)	.947(1.41)	.949(1.39)	.940(1.37)	.946(1.13)	.952(1.15)	.945(1.12)	.947(1.13)
	Wald	M-Wald	Likelihood	Score	Wald	M-Wald	Likelihood	Score
$\mu =10$
n	$\theta =.5$				$\theta =1$
10	–	–	–	–	.875(12.0)	.922(15.4)	.875(12.1)	.896(20.7)
20	.880(11.8)	.901(13.1)	.884(12.3)	.928(19.1)	.909(8.76)	.928(9.75)	.915(8.91)	.941(11.2)
30	.903(9.92)	.917(10.6)	.914(10.2)	.942(14.1)	.920(7.31)	.935(7.83)	.926(7.38)	.943(8.51)
40	.909(8.66)	.920(9.11)	.918(8.88)	.946(11.0)	.926(6.36)	.936(6.69)	.931(6.41)	.942(7.11)
50	.920(7.80)	.929(8.12)	.930(7.98)	.945(9.47)	.931(5.70)	.940(5.93)	.936(5.75)	.943(6.24)
60	.920(7.16)	.927(7.40)	.928(7.28)	.946(8.37)	.935(5.23)	.942(5.40)	.938(5.27)	.946(5.63)
70	.924(6.64)	.931(6.83)	.931(6.75)	.947(7.59)	.933(4.84)	.939(4.98)	.938(4.87)	.946(5.16)
80	.930(6.23)	.936(6.39)	.941(6.32)	.946(7.00)	.938(4.53)	.943(4.64)	.942(4.55)	.948(4.78)
90	.926(5.86)	.931(5.99)	.932(5.94)	.947(6.50)	.940(4.28)	.945(4.38)	.940(4.30)	.948(4.49)
n	$\theta =4$				$\theta =10$
10	.912(7.14)	.961(9.09)	.905(6.92)	.915(7.75)	.939(5.65)	.978(7.20)	.929(5.42)	.932(5.69)
20	.923(5.08)	.947(5.66)	.921(5.01)	.928(5.27)	.935(3.90)	.957(4.34)	.929(3.82)	.931(3.91)
30	.932(4.18)	.949(4.48)	.930(4.15)	.936(4.29)	.939(3.17)	.953(3.39)	.937(3.13)	.937(3.17)
40	.939(3.62)	.950(3.81)	.939(3.59)	.942(3.68)	.943(2.75)	.954(2.89)	.941(2.72)	.942(2.75)
50	.943(3.24)	.951(3.37)	.943(3.22)	.945(3.29)	.939(2.46)	.949(2.56)	.938(2.44)	.940(2.46)
60	.939(2.97)	.946(3.07)	.938(2.95)	.945(3.00)	.945(2.25)	.952(2.33)	.943(2.23)	.946(2.25)
70	.948(2.75)	.954(2.83)	.948(2.74)	.948(2.78)	.945(2.08)	.950(2.14)	.943(2.07)	.945(2.08)
80	.944(2.57)	.949(2.64)	.943(2.57)	.944(2.60)	.946(1.95)	.950(2.00)	.945(1.94)	.946(1.95)
90	.945(2.42)	.949(2.48)	.945(2.41)	.946(2.44)	.946(1.84)	.952(1.88)	.945(1.83)	.945(1.84)
$\mu =20$
n	$\theta =.5$				$\theta =1$
10	–	–	–	–	.875(23.5)	.923(29.9)	.898(42.2)	.870(23.5)
20	.883(23.3)	.905(25.9)	.892(24.3)	.933(42.7)	.906(17.2)	.928(19.1)	.909(17.4)	.930(21.8)
30	.901(19.4)	.916(20.8)	.910(20.1)	.941(27.4)	.917(14.2)	.931(15.2)	.921(14.4)	.943(16.5)
40	.915(17.1)	.927(18.0)	.924(17.6)	.946(21.9)	.926(12.3)	.936(13.0)	.933(12.5)	.940(13.8)
50	.918(15.3)	.926(16.0)	.925(15.7)	.947(18.6)	.931(11.1)	.939(11.5)	.934(11.2)	.948(12.1)
60	.921(14.1)	.927(14.6)	.929(14.4)	.945(16.5)	.932(10.2)	.939(10.5)	.936(10.2)	.946(10.9)
70	.927(13.0)	.932(13.4)	.935(13.4)	.952(15.0)	.940(9.47)	.944(9.74)	.940(9.52)	.947(10.0)
80	.926(12.2)	.932(12.5)	.932(12.4)	.949(13.7)	.937(8.86)	.943(9.08)	.939(8.90)	.948(9.35)
90	.930(11.6)	.934(11.9)	.936(11.7)	.948(12.8)	.939(8.37)	.943(8.56)	.942(8.41)	.948(8.79)
n	$\theta =4$				$\theta =10$
10	.905(12.9)	.956(16.5)	.896(12.5)	.906(13.8)	.923(9.46)	.968(12.0)	.910(9.05)	.914(9.44)
20	.921(9.38)	.944(10.4)	.919(9.24)	.929(9.71)	.931(6.71)	.953(7.46)	.925(6.57)	.926(6.71)
30	.930(7.71)	.944(8.26)	.929(7.65)	.938(7.90)	.941(5.48)	.955(5.87)	.938(5.41)	.940(5.48)
40	.937(6.70)	.949(7.04)	.936(6.65)	.940(6.82)	.938(4.76)	.949(5.01)	.937(4.71)	.938(4.76)
50	.938(6.02)	.948(6.26)	.939(5.98)	.943(6.10)	.945(4.26)	.955(4.43)	.944(4.23)	.945(4.26)
60	.941(5.51)	.947(5.70)	.939(5.48)	.941(5.57)	.941(3.90)	.949(4.03)	.940(3.87)	.940(3.90)
70	.942(5.10)	.948(5.24)	.944(5.08)	.945(5.15)	.941(3.60)	.948(3.71)	.939(3.58)	.943(3.60)
80	.945(4.77)	.950(4.89)	.945(4.75)	.945(4.81)	.946(3.38)	.951(3.46)	.945(3.36)	.945(3.37)
90	.949(4.50)	.954(4.60)	.948(4.49)	.948(4.54)	.947(3.19)	.952(3.26)	.947(3.17)	.945(3.18)