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Survival and density function analysis in R, Assignments of Applied Mathematics

Kwame Nkrumah University of Science and TechnologyApplied Mathematics

We are to find the survival function, density function, and hazard function for Gompertz, Makeham, Weibull, Exponential and DeMoivre and plot the graphs for each at x = 20, x = 50 and x = 80 using R studio

Typology: Assignments

2025/2026

Uploaded on 02/12/2026

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Page 1 of 1 C. ABAITEY
2023/2024 ACADEMIC YEAR
ACTS 351: LIFE CONTINGENCIES I
PRACTICAL SESSIONS (15points)
ASSIGNMENT 1
NOTE:
1. Use the R statistical software to complete this assignment.
2. Submission: From February 14, 2024 to February 15, 2024.
REFERENCE: See pages 43 – 44 of the pdf (Actuarial Mathematics for Life Contingent
Risks, 3rd ed.); which can be found on our V-class platform.
Calculate the survival function and probability density function for T(x) using:
a) Gompertz’ law of mortality, with B = 0.0003 and c = 1.07, for x = 20, x = 50 and x = 80.
Plot the results and comment on the features of the graphs.
b) Makeham’s law of mortality, with A = 0.00022, B = 0.0000027 and c = 1.124, for x = 20,
x = 50 and x = 80. Plot the results and comment on the features of the graphs.
c) Weibull’s law of mortality, with k = 5 and n = 1, for x = 20, x = 50 and x = 80. Plot the
results and comment on the features of the graphs.
d) Generalized De Moivre’s law of mortality, with α = 0.5 and ω = 90 for x = 20, x = 50 and
x = 80. Plot the results and comment on the features of the graphs.
e) Constant force of mortality with µ = 0.02 for x = 20, x = 50 and x = 80. Plot the results and
comment on the features of the graphs.

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Page 1 of 1 C. ABAITEY

2023/2024 ACADEMIC YEAR

ACTS 351: LIFE CONTINGENCIES I

PRACTICAL SESSIONS ( 1 5points) ASSIGNMENT 1 NOTE:

  1. Use the R statistical software to complete this assignment.
  2. Submission: From February 14, 2024 to February 15, 2024. REFERENCE : See pages 43 – 44 of the pdf ( Actuarial Mathematics for Life Contingent Risks, 3rd^ ed. ); which can be found on our V-class platform. Calculate the survival function and probability density function for T(x) using: a) Gompertz’ law of mortality, with B = 0.0003 and c = 1.07, for x = 20, x = 50 and x = 80. Plot the results and comment on the features of the graphs. b) Makeham’s law of mortality, with A = 0.00022, B = 0.0000027 and c = 1.124, for x = 20, x = 50 and x = 80. Plot the results and comment on the features of the graphs. c) Weibull’s law of mortality, with k = 5 and n = 1, for x = 20, x = 50 and x = 80. Plot the results and comment on the features of the graphs. d) Generalized De Moivre’s law of mortality, with α = 0. 5 and ω = 90 for x = 20, x = 50 and x = 80. Plot the results and comment on the features of the graphs. e) Constant force of mortality with μ = 0.02 for x = 20, x = 50 and x = 80. Plot the results and comment on the features of the graphs.