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Table 3 Bias and standard deviation for maximum likelihood estimates

From: The Kumaraswamy-geometric distribution

 

Actual values

Bias with standard deviation in parentheses

 

n

α

β

q

α ^

β ^

q ^

Mode

250

1.6

2.0

0.6

-0.1295(0.2099)

0.1128(0.4697)

0.0409(0.0733)

0

 

4.0

2.0

0.4

-0.3136(0.7844)

0.1047(0.4617)

0.0237(0.0698)

1

 

4.0

2.0

0.6

-0.1977(0.5714)

0.1021(0.4571)

0.0198(0.0571)

2

 

4.0

2.0

0.8

-0.2467(0.5521)

0.0852(0.4020)

0.0126(0.0293)

4

 

6.0

4.0

0.8

-0.3931(0.8570)

0.2084(0.9507)

0.0121(0.0278)

5

500

1.6

2.0

0.6

-0.0437(0.1436)

0.0121(0.4496)

0.0153(0.0665)

0

 

4.0

2.0

0.4

-0.3142(0.5876)

0.1383(0.4421)

0.0290(0.0639)

1

 

4.0

2.0

0.6

-0.2015(0.4728)

0.0808(0.4504)

0.0194(0.0527)

2

 

4.0

2.0

0.8

-0.2747(0.4630)

0.1526(0.3781)

0.0157(0.0278)

4

 

6.0

4.0

0.8

-0.3283(0.7771)

0.2187(0.9375)

0.0116(0.0267)

5

750

1.6

2.0

0.6

-0.0533(0.1305)

0.1184(0.4250)

0.0278(0.0669)

0

 

4.0

2.0

0.4

-0.3181(0.5939)

0.1707(0.4195)

0.0328(0.0622)

1

 

4.0

2.0

0.6

-0.1787(0.4775)

0.0562(0.4469)

0.0159(0.0522)

2

 

4.0

2.0

0.8

-0.1717(0.4739)

0.0813(0.4117)

0.0101(0.0299)

4

 

6.0

4.0

0.8

-0.2472(0.5940)

0.1947(0.8090)

0.0087(0.0227)

5