PoissonDistribution
LogNormalDistribution
CensoredDistribution
MarginalDistribution
NormalDistribution
ExponentialDistribution
UniformDistribution
TransformedDistribution
Probability
Expectation
SurvivalFunction
Variance
Solve
ProductDistribution
PDF

Probability & Statistics
Finance & Economics
Data Science

Actuarial Analysis of Insurance Policies

Illustrate how common insurance scenarios can be modeled using standard probability distributions

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Automobile Accident Age
(5)

Let 𝑥 be the age (in years) of an insured automobile at the time of an accident, and let 𝑦 be the length of time the automobile has been insured. The joint density of (𝑥, 𝑦) is (𝑥, 𝑦) =

10-

𝑥𝑦

defined for 𝑥 ∈ [2, 10], 𝑦 ∈ [0, 1]. Find the expected age of an insured automobile involved in an accident.

Let the joint probability density be:

In[1]:=

ageDistribution=ProbabilityDistribution[(10-xy^2)/64,{x,2,10},{y,0,1}];

Compute the expected value of the automobile age:

In[2]:=

expAge=Expectation[x,{x,y}ageDistribution]

Out[2]=

Visualize the joint density:

In[3]:=

Plot3D[(10-xy^2)/64,{x,2,10},{y,0,1},PlotRangeAll,AxesLabel{"x (Age)","y (Coverage)","PDF"},PlotTheme"Scientific",MeshNone]

Out[3]=

Show a cross-section of the marginal PDF of 𝑥:

In[4]:=

margX=MarginalDistribution[ageDistribution,1];Plot[PDF[margX,t],{t,2,10},FrameTrue,FrameLabel{"x (Age)","Density"},PlotTheme"Scientific"]

Out[4]=

Do the same for 𝑦:

In[5]:=

margY=MarginalDistribution[ageDistribution,2];Plot[PDF[margY,s],{s,0,1},FrameTrue,FrameLabel{"y (Coverage Duration)","Density"},PlotTheme"Scientific"]

Out[5]=

Censored Benefit
(5)



Claim variance
(4)



Claim values I
(3)



Claim values II
(3)



Excess-of-Loss
(5)



Good versus bad driver
(4)



Maximum wind claim
(6)



Monthly claims
(5)



Related Symbols

PoissonDistribution
LogNormalDistribution
CensoredDistribution
MarginalDistribution
NormalDistribution
ExponentialDistribution
UniformDistribution
TransformedDistribution
Probability
Expectation
SurvivalFunction
Variance
Solve
ProductDistribution
PDF

Publisher Information

Contributed by: Wolfram Staff

Actuarial Analysis of Insurance Policies

Automobile Accident Age (5)

Censored Benefit (5) 

Claim variance (4) 

Claim values I (3) 

Claim values II (3) 

Excess-of-Loss (5) 

Good versus bad driver (4) 

Maximum wind claim (6) 

Monthly claims (5) 