Car survival in a national car fleet : Non-parametric and parametric approaches applied to french data

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We aim to determine the common demographic conditions and variables that affect light cars survival in the national fleet. The essential aim is to identify which variables determine cars’ longevity and to understand how it can be measured. Therefore in this study two fundamental questions are asked: -'What are the main determinants of cars’ longevity?'. -'Can we consider car mileage as a major dimension of cars’ longevity?'.To give an answer, we adopted a longitudinal analysis based on panel data. Yearly French 'Parc-Auto' waves were linked together from 2000 up to 2006 to make a 7-year panel, with 6795 cars described. Variables like car age, total mileage, car status (i.e., whether the car is unique, main or secondary in the household) and motorization (i.e., gasoline or diesel) are used. In order to have an overview on car survival, we consider a new approach by building and comparing Kaplan-Meier survival curves by car age and by average monthly mileage. The idea is to compare car use measured by the average monthly mileage with car's life expectancy measured by age, and to conclude for each determinant (i.e., status and motorization) about how intensity of use is linked to car longevity. As we do not have data concerning car scrapping or disappearing from the fleet; all observations are right censored. We show that mortality risk increases for all car categories with age and mileage. Gasoline cars have a better survival rate than diesel cars. Car status is also a major determinant of car survival: secondary cars have better survival rates than main cars or than unique cars. This is explained by the fact that sole cars are used more extensively than main or secondary cars. Bivariate pdf (i.e., probability density functions) described by age and total mileage helps to show that this phenomenon has to be related to an extensive use of diesel cars and of cars declared as to be sole in the household (i.e., versus 'main' or 'secondary' cars). To complete this approach we choose to proceed to a parametric study in order to find the best functional shape for the car age and car mileage statistical distributions. Models were estimated using three-parameters- Beta, Gamma, Lognormal and Weibull distributions. Adequacy parameters and qq-plots show that the Beta and Weibull distributions are the best compared to all other models. Therefore, Beta and Weibull are good candidates to represent cars’ survival laws. More importantly, this study shows that car mileage defined as a marker process is a major dimension to describe cars’ longevity.