3. A certain actuarial model of mortality rate is fitted to some given data. Table 2 below reports the Z-score statistic of the model graduation. (a) List the key steps involved in developing an actuarial model. (b) Explain why we need graduation. What do we actually test statistically? (c) What are the drawbacks of a x²- test? Explain how the sign test may overcome these. (d) Write a statistical hypothesis to test the adherence of the model to the data
3. A certain actuarial model of mortality rate is fitted to some given data. Table 2 below reports the Z-score statistic of the model graduation. (a) List the key steps involved in developing an actuarial model. (b) Explain why we need graduation. What do we actually test statistically? (c) What are the drawbacks of a x²- test? Explain how the sign test may overcome these. (d) Write a statistical hypothesis to test the adherence of the model to the data
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![3. A certain actuarial model of mortality rate is fitted to some given data. Table 2 below
reports the Z-score statistic of the model graduation.
(a) List the key steps involved in developing an actuarial model.
(b) Explain why we need graduation. What do we actually test statistically?
(c) What are the drawbacks of a x²- test? Explain how the sign test may overcome
these.
(d) Write a statistical hypothesis to test the adherence of the model to the data.
(e) The life table data below provides an estimate of mortality rates obtained from
a three-parameter Poisson model. Give the quality of goodness-of-fit of the Poisson
model by performing statistical tests based on:, and draw the conclusions.
i. x²-test.
ii. Standardized deviations test. [Consider the following subintervals for the data
range: A₁ = (-∞, −3], A₂ = (−3,−2], A3 = (−2, −1], A4 = (–1, 0], A5 = (0, 1],
A6 = (1, 2], A7 = (2, 3], and Ag = (3, ∞).]
iii. Sign test
iv. Change-of-sign test
v. Grouping-of-sign test
vi. Lag-2 serial correlation test
Age(x) lx dx
λº (x10-³)
Zx
12
8119 14
2.3131
-1.09976140
7750 20 2.5394
0.07782846
0.73850019
6525 22 2.8858
5998 23 3.3961
0.59198689
5586 26
0.61533059
4.1353
5.2145
5245 28
0.13842351
4659 32
6.8040
0.07277321
4222 37
9.1829
-0.25757957
3660 44
12.8197
-0.38629208
3012 54
18.4927
-0.16160903
2500 68
27.5240
0.01527157
2113 87 42.1675
-0.02843635
1469 100 66.2083
0.62422085
883 95 105.7305
0.70883012
418 70
169.5455
0.62843083
181 49 267.4033
1.10547651
Table 2: Tabel of mortality rates.
!
17
22
27
32
37
42
47
52
62
67
72
77
82
87](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33d8b77c-c45c-4683-a846-399089840e36%2Fd164a626-7620-4d60-af78-9b3c95e12764%2Fmglkq1o_processed.png&w=3840&q=75)
Transcribed Image Text:3. A certain actuarial model of mortality rate is fitted to some given data. Table 2 below
reports the Z-score statistic of the model graduation.
(a) List the key steps involved in developing an actuarial model.
(b) Explain why we need graduation. What do we actually test statistically?
(c) What are the drawbacks of a x²- test? Explain how the sign test may overcome
these.
(d) Write a statistical hypothesis to test the adherence of the model to the data.
(e) The life table data below provides an estimate of mortality rates obtained from
a three-parameter Poisson model. Give the quality of goodness-of-fit of the Poisson
model by performing statistical tests based on:, and draw the conclusions.
i. x²-test.
ii. Standardized deviations test. [Consider the following subintervals for the data
range: A₁ = (-∞, −3], A₂ = (−3,−2], A3 = (−2, −1], A4 = (–1, 0], A5 = (0, 1],
A6 = (1, 2], A7 = (2, 3], and Ag = (3, ∞).]
iii. Sign test
iv. Change-of-sign test
v. Grouping-of-sign test
vi. Lag-2 serial correlation test
Age(x) lx dx
λº (x10-³)
Zx
12
8119 14
2.3131
-1.09976140
7750 20 2.5394
0.07782846
0.73850019
6525 22 2.8858
5998 23 3.3961
0.59198689
5586 26
0.61533059
4.1353
5.2145
5245 28
0.13842351
4659 32
6.8040
0.07277321
4222 37
9.1829
-0.25757957
3660 44
12.8197
-0.38629208
3012 54
18.4927
-0.16160903
2500 68
27.5240
0.01527157
2113 87 42.1675
-0.02843635
1469 100 66.2083
0.62422085
883 95 105.7305
0.70883012
418 70
169.5455
0.62843083
181 49 267.4033
1.10547651
Table 2: Tabel of mortality rates.
!
17
22
27
32
37
42
47
52
62
67
72
77
82
87
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