12. Household content insurance claims are modeled by a Weibull distribu- tion with parameters c> 0 and y=2. (a) A random sample of 50 such claims yields 50 50 = 13,500 and 1 4,500,000. Calculate the method of moments estimator ē and the method of maximum likelihood estimate ĉ of c using this information. Determine an approximate 95% confidence interval for e based on maximum likelihood. TABLE 2.8 Portfolio of 120 claims. Observed Expected Interval Oi E(Exp) E (Weibull) 1234567 0, 7.90] 12 2.12 27.90, 16.74] 9 12 7.11 16.74, 26.75 14 12 12.95 26.75, 38.31] 16 12 18.91 38.31, 51.99 21 12 23.46 51.99, 68.72] 22 12 24.30 68.72, 90.30] 18 12 19.45 8 90.30, 103.97] 7 ? ? 9 103.97, 172.69 8 ? ? 10 172.69, +00 1 ? ? (b) If a deductible of 200 is introduced, estimate (using maximum like- lihood) the reduction in the proportion of claims to be made.
12. Household content insurance claims are modeled by a Weibull distribu- tion with parameters c> 0 and y=2. (a) A random sample of 50 such claims yields 50 50 = 13,500 and 1 4,500,000. Calculate the method of moments estimator ē and the method of maximum likelihood estimate ĉ of c using this information. Determine an approximate 95% confidence interval for e based on maximum likelihood. TABLE 2.8 Portfolio of 120 claims. Observed Expected Interval Oi E(Exp) E (Weibull) 1234567 0, 7.90] 12 2.12 27.90, 16.74] 9 12 7.11 16.74, 26.75 14 12 12.95 26.75, 38.31] 16 12 18.91 38.31, 51.99 21 12 23.46 51.99, 68.72] 22 12 24.30 68.72, 90.30] 18 12 19.45 8 90.30, 103.97] 7 ? ? 9 103.97, 172.69 8 ? ? 10 172.69, +00 1 ? ? (b) If a deductible of 200 is introduced, estimate (using maximum like- lihood) the reduction in the proportion of claims to be made.
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![12. Household content insurance claims are modeled by a Weibull distribu-
tion with parameters c> 0 and y=2.
(a) A random sample of 50 such claims yields
50
50
= 13,500 and
1
4,500,000. Calculate the method of moments estimator ē
and the method of maximum likelihood estimate ĉ of c using this
information. Determine an approximate 95% confidence interval
for e based on maximum likelihood.
TABLE 2.8
Portfolio of 120 claims.
Observed
Expected
Interval
Oi
E(Exp) E (Weibull)
1234567
0, 7.90]
12
2.12
27.90, 16.74]
9
12
7.11
16.74, 26.75
14
12
12.95
26.75, 38.31]
16
12
18.91
38.31, 51.99
21
12
23.46
51.99, 68.72]
22
12
24.30
68.72, 90.30]
18
12
19.45
8 90.30, 103.97]
7
?
?
9
103.97, 172.69
8
?
?
10
172.69, +00
1
?
?
(b) If a deductible of 200 is introduced, estimate (using maximum like-
lihood) the reduction in the proportion of claims to be made.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba18de34-fc06-47a6-b1ea-c54726b84874%2Ff733fcb7-2286-4264-8896-d892b9974f11%2F8hxlkx3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:12. Household content insurance claims are modeled by a Weibull distribu-
tion with parameters c> 0 and y=2.
(a) A random sample of 50 such claims yields
50
50
= 13,500 and
1
4,500,000. Calculate the method of moments estimator ē
and the method of maximum likelihood estimate ĉ of c using this
information. Determine an approximate 95% confidence interval
for e based on maximum likelihood.
TABLE 2.8
Portfolio of 120 claims.
Observed
Expected
Interval
Oi
E(Exp) E (Weibull)
1234567
0, 7.90]
12
2.12
27.90, 16.74]
9
12
7.11
16.74, 26.75
14
12
12.95
26.75, 38.31]
16
12
18.91
38.31, 51.99
21
12
23.46
51.99, 68.72]
22
12
24.30
68.72, 90.30]
18
12
19.45
8 90.30, 103.97]
7
?
?
9
103.97, 172.69
8
?
?
10
172.69, +00
1
?
?
(b) If a deductible of 200 is introduced, estimate (using maximum like-
lihood) the reduction in the proportion of claims to be made.
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