• Introduction
• Part One: data set view,summary-descriptive analysis
  • data set dimensions
  • Data set variables types
  • Data set summary and distribution
    • Numerical variables
    • Categotical variables
• Part Two: insurance risk measurements by factors.
  • gender factor
  • veh_age factor
  • veh_body
  • area
  • age category
• Part Three: claims count response to the predictors variables
• Part four: rating factors
• Conclusion:
  • preferred segments
  • the high risk segments

Introduction

This analysis is conducted by using R-programming language as an analysis tool in the insurance industry, and specially for motor insurance .

The data set used called (datacar) and can be found on the (insurancedata) package on r.

>we have also used packages such as:
- tidyvarse.
- tidyr.
- janitor.
- knitr.
- insurancerating , and others.

>what we are going to do ?

• looking at the data summary and description on order to understand the shape of the data.

• calculating the claims cost and group it by factors.

• calculating the claims count and group it by factors.

• calculating the total exposure and group it by factors.

• calculating the frequency cost and group it by factors.

• calculating the average severity cost and group it by factors.

• calculating the pure premium cost and group it by factors.

• calculating the rating factor for each.

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Part One: data set view,summary-descriptive analysis

data set dimensions

lets have a look at the data set dimension :

## [1] 67856    10

the data set has 10 variables and and 67856 rows , the 1st 5 rows are as below :

Data set variables types

lets have a look at the variables types:

## Rows: 67,856
## Columns: 10
## $ veh_value <dbl> 1.06, 1.03, 3.26, 4.14, 0.72, 2.01, 1.60, 1.47, 0.52, 0.38, …
## $ exposure  <dbl> 0.30390144, 0.64887064, 0.56947296, 0.31759069, 0.64887064, …
## $ clm       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, …
## $ numclaims <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, …
## $ claimcst0 <dbl> 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.00…
## $ veh_body  <fct> HBACK, HBACK, UTE, STNWG, HBACK, HDTOP, PANVN, HBACK, HBACK,…
## $ veh_age   <int> 3, 2, 2, 2, 4, 3, 3, 2, 4, 4, 2, 3, 2, 1, 3, 2, 3, 3, 4, 3, …
## $ gender    <fct> F, F, F, F, F, M, M, M, F, F, M, M, F, M, M, M, F, M, F, F, …
## $ area      <fct> C, A, E, D, C, C, A, B, A, B, A, C, C, A, B, C, F, C, D, C, …
## $ agecat    <int> 2, 4, 2, 2, 2, 4, 4, 6, 3, 4, 2, 4, 4, 5, 6, 4, 4, 4, 2, 3, …

now we will make some data transformation,will do the below :

1. convert agecat & veh_age types into factor

2. create a new variable called: veh_value_group

lets look again to the variables types :

## Rows: 67,856
## Columns: 11
## $ veh_value       <dbl> 1.06, 1.03, 3.26, 4.14, 0.72, 2.01, 1.60, 1.47, 0.52, …
## $ exposure        <dbl> 0.30390144, 0.64887064, 0.56947296, 0.31759069, 0.6488…
## $ clm             <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, …
## $ numclaims       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, …
## $ claimcst0       <dbl> 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000…
## $ veh_body        <fct> HBACK, HBACK, UTE, STNWG, HBACK, HDTOP, PANVN, HBACK, …
## $ veh_age         <fct> 3, 2, 2, 2, 4, 3, 3, 2, 4, 4, 2, 3, 2, 1, 3, 2, 3, 3, …
## $ gender          <fct> F, F, F, F, F, M, M, M, F, F, M, M, F, M, M, M, F, M, …
## $ area            <fct> C, A, E, D, C, C, A, B, A, B, A, C, C, A, B, C, F, C, …
## $ agecat          <fct> 2, 4, 2, 2, 2, 4, 4, 6, 3, 4, 2, 4, 4, 5, 6, 4, 4, 4, …
## $ veh_value_group <fct> group 1, group 1, group 1, group 1, group 1, group 1, …

Data set summary and distribution

lets have the data summary and the variables distribution :

Numerical variables

• the vehicle value range is between 0 and 34,560 with 1,777 on average

• the exposure range is between 0 and 1 with 0.44 on average

• the claims cost range is between 0 and 55,922.1 with 137,3 on average

Categotical variables

• 7% of the vehicles in this data had claims .

• 43% of the data samples are for males and 57% are for females.

• more than 50% of our vehicles are old (3 & 4 ages) and only 18% are brand new vehicles.

• area C has the highest number of customers with 30 % , and area F has the lowest 5%.

• more than 45% of the customers are located in the age group 3 & 4.

• more than 99% of our vehicles values are within group 1.

• sedan vehicles has the highest percentage with 32% ,and (Bus,CONVT,MCARA,RDSTR) has the lowest with less than 1%.

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Part Two: insurance risk measurements by factors.

as the insurance risk level is measured by the frequency and the severity; we will calculate the the same and group it by factors.

gender factor

we can see that :

• females number of claims are more than males.

• females claims cost are more than males but; the average severity is less ,and this is due to the larger number of claims(more than males)

• both females and males almost have the same frequency.

• female risk premium is lesser than males ,and this due to the higher exposure females have.

the below chart visualize all together for more clear understanding:

veh_age factor

we can see that :

• the claims cost for the vehicle age 1 is the lowest while for vehicle age 3 is the highest.

• vehicle age 1 has the lowest number on claims while the vehicle age 3 has the highest.

• the exposure for the vehicle age 1 is the lowest while for vehicle age 3 is the highest.

• the frequency for the vehicle age 4 is the lowest while for vehicle age 2 is the highest.

• the average_severity for the vehicle age 1 is the lowest while for vehicle age 4 is the highest.

• the risk premium for the vehicle age 3 & 4 is the lowest and almost the same, while its the highest for vehicle age 2

the below chart visualize all together for more clear understating :

veh_body

We can see that:

• sedan,Hback,and Stnwg have the highest claims cost (), while RDSTR has the lowest claims cost.

• RDSTR ,convt,Bus,MCARA,COUPE & PANVN have less than 100 claims, SEDAN,STNWG & HBACK have more than 1000 claims ,other have claims between 130 and 276.

• BUS has the highest frequency with 38.3% , (RDSTR,MCARA, and COUPE have frequincies (27.7%,25.3% and 23.5%), other groups have frequencies less than 18%.

• RDSTR has the lowest average severity , (MIBUS,COUPE and TRUCK ) have the highest.

• the risk premium is the less than 200 for RDSTR and MCARA, the more tgan 500 for BUS and COUPE.

the below chart visualize all together for more clear understanding:

area

we can see that :

• the lowest claims cost is for area F , and the highest cost is for area C.

• area F has the lowest number of claims , while area C has the highest .

• area D has the lowest frequency , while area F has the highest.

• area D has the lowest average frequency ,while area F has the highest.

• area D has the lowest risk premium , while area F has the highest.

the below chart visualize all together for more clear understanding:

age category

we can see that :

• age category 6 has the lowest claims cost , while age category 4 has the highest

• age category 6 has the lowest number of claims , while age category 4 & 3 has the highest (1185,1189) .

• age category 6 & 5 has the lowest frequency with almost(12.5%) , while age category 1 has the highest with 20%.

• age category 5 has the lowest average frequency ,while age category 1 has the highest.

• age category 5 has the lowest risk premium , while age category 1 has the highest.

the below chart visualize all together for more clear understanding:

now, lets create a new model that contains all factor variables and see how much it differs from the previous models and which one is the best.

## $statistics
##                           aic      bic bayes.factor      p
## numclaims_glm_all    34822.37 35068.75 0.000000e+00 <2e-16
## numclaims_glm_agecat 34862.03 34916.78 1.002062e+33       
## 
## $predicted_differences
##    0%   25%   50%   75%  100% 
## 0.000 0.001 0.004 0.009 0.247

## $statistics
##                         aic      bic bayes.factor      p
## numclaims_glm_all  34822.37 35068.75 0.000000e+00 <2e-16
## numclaims_glm_area 34938.22 34992.97 2.858943e+16       
## 
## $predicted_differences
##    0%   25%   50%   75%  100% 
## 0.000 0.002 0.006 0.014 0.284

## $statistics
##                           aic      bic bayes.factor      p
## numclaims_glm_all    34822.37 35068.75 0.000000e+00 <2e-16
## numclaims_glm_gender 34944.03 34962.28 1.317565e+23       
## 
## $predicted_differences
##    0%   25%   50%   75%  100% 
## 0.000 0.002 0.007 0.015 0.282

## $statistics
##                            aic      bic bayes.factor      p
## numclaims_glm_all     34822.37 35068.75 0.000000e+00 <2e-16
## numclaims_glm_veh_age 34920.50 34957.00 1.850433e+24       
## 
## $predicted_differences
##    0%   25%   50%   75%  100% 
## 0.000 0.002 0.006 0.013 0.287

## $statistics
##                             aic      bic bayes.factor      p
## numclaims_glm_all      34822.37 35068.75         0.00 <2e-16
## numclaims_glm_veh_body 34930.11 35048.74     22196.62       
## 
## $predicted_differences
##    0%   25%   50%   75%  100% 
## 0.000 0.002 0.006 0.014 0.132

from our results we can say that the numclaims_glm_all model is best .

lets apply the anova function on the model so we can well know how much the variables are important to the model

## Analysis of Deviance Table
## 
## Model: poisson, link: log
## 
## Response: numclaims
## 
## Terms added sequentially (first to last)
## 
## 
##          Df Deviance Resid. Df Resid. Dev  Pr(>Chi)    
## NULL                     67855      25507              
## veh_body 12   37.563     67843      25469  0.000181 ***
## veh_age   3   33.543     67840      25436 2.474e-07 ***
## gender    1    1.595     67839      25434  0.206575    
## area      5   14.525     67834      25420  0.012598 *  
## agecat    5   86.074     67829      25334 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The drop in deviance allows to test whether the model terms are significant :

• adding veh_body to the NULL model causes a drop in deviance of 37.563 corresponding to 67843 degree of freedom and resulting residual deviance of 25469

• adding veh_age to the NULL model causes a drop in deviance of 33.543 corresponding to 67840 degree of freedom and resulting residual deviance of 25436

• adding gender to the NULL model causes a drop in deviance of 1.595 corresponding to 67839 degree of freedom and resulting residual deviance of 25434

• adding area to the NULL model causes a drop in deviance of 14.525 corresponding to 67834 degree of freedom and resulting residual deviance of 25420

• adding agecat to the NULL model causes a drop in deviance of 86.074 corresponding to 68729 degree of freedom and resulting residual deviance of 25334

so the gender variable has the least impact on the model

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Part Three: claims count response to the predictors variables

the below chart express visually how number of claims will act (decrease on increase)-along with the lower and upper confident intervals-, when any of the factors increase by one unit:

if any factor increases by one unit ;the number of claims will increase or decrease by the coefficient value for the same factor.

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Part four: rating factors

now;lets look at the rating factor for the new model (numclaims_glm_all) which is the best performed model:

## Significance levels: *** p < 0.001; ** p < 0.01;
##     * p < 0.05; . p < 0.1

on graph:

## Significance levels: *** p < 0.001; ** p < 0.01;
##     * p < 0.05; . p < 0.1

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Conclusion:

preferred segments

• area : D.

• agecat : 5,6

• veh_body : UTE,CONVT.

the high risk segments

• veh_body : BUS,COUPE,MACARA,RDSTS