Data Mining in Automotive Warranty Analysis

<p>This thesis is about data mining in automotive warranty analysis, with an emphasis on modeling the mean cumulative warranty cost or number of claims (per vehicle). In our study, we deal with a type of truncation that is typical for automotive warranty data, where the warranty coverage and the resulting warranty data are limited by age and mileage. Age, as a function of time, is known for all sold vehicles at all time. However, mileage is only observed for a vehicle with at least one claim and only at the time of the claim. To deal with this problem of incomplete mileage information, we consider a linear approach and a piece-wise linear approach within a nonparametric framework. We explore the univariate case, as well as the bivariate case. For the univariate case, we evaluate the mean cumulative warranty cost and its standard error as a function of age, a function of mileage, and a function of actual (calendar) time. For the bivariate case, we evaluate the mean cumulative warranty cost as a function of age and mileage. The effect of reporting delay of claim and several methods for making prediction are also considered. Throughout this thesis, we illustrate the ideas using examples based on real data.</p>

Data Mining in Automotive Warranty Analysis

<p>This thesis is about data mining in automotive warranty analysis, with an emphasis on modeling the mean cumulative warranty cost or number of claims (per vehicle). In our study, we deal with a type of truncation that is typical for automotive warranty data, where the warranty coverage and the resulting warranty data are limited by age and mileage. Age, as a function of time, is known for all sold vehicles at all time. However, mileage is only observed for a vehicle with at least one claim and only at the time of the claim. To deal with this problem of incomplete mileage information, we consider a linear approach and a piece-wise linear approach within a nonparametric framework. We explore the univariate case, as well as the bivariate case. For the univariate case, we evaluate the mean cumulative warranty cost and its standard error as a function of age, a function of mileage, and a function of actual (calendar) time. For the bivariate case, we evaluate the mean cumulative warranty cost as a function of age and mileage. The effect of reporting delay of claim and several methods for making prediction are also considered. Throughout this thesis, we illustrate the ideas using examples based on real data.</p>

A Family of the r-Associated Stirling Numbers of the Second Kind and Generalized Bernoulli Polynomials

In this article, we derive representation formulas for a class of r-associated Stirling numbers of the second kind and examine their connections with a class of generalized Bernoulli polynomials. Herein, we use the Blissard umbral approach and the familiar Bell polynomials. Links with available literature on this subject are also pointed out. The extension to the bivariate case is discussed.

Quadratic transformation of multivariate aggregation functions

In this work, we prove that quadratic transformations of aggregation functions must come from quadratic aggregation functions. We also show that this is different from quadratic transformations of (multivariate) semi-copulas and quasi-copulas. In the latter case, those two classes are actually the same and consists of convex combinations of the identity map and another fixed quadratic transformation. In other words, it is a convex set with two extreme points. This result is different from the bivariate case in which the two classes are different and both are convex with four extreme points.

On Some Properties of Copula-Based Partial Moments

Partial moments are extensively used in the field of analysis of risks. This paper aims at extending it to the bivariate case based on copula function and study its various properties. The relationship between survival copula and first-order bivariate partial moments are established. We also investigate some applications of copula-based partial moments and conditional partial moments in the context of reliability, income and actuarial studies.

Weighted statistical approximation properties of univariate and bivariate λ-Kantorovich operators

In this study, we consider statistical approximation properties of univariate and bivariate ?-Kantorovich operators. We estimate rate of weighted A-statistical convergence and prove a Voronovskajatype approximation theorem by a family of linear operators using the notion of weighted A-statistical convergence. We give some estimates for differences of ?-Bernstein and ?-Durrmeyer, and ?-Bernstein and ?-Kantorovich operators. We establish a Voronovskaja-type approximation theorem by weighted A-statistical convergence for the bivariate case.

Regression

This chapter presents the logic and technique of analyzing data using simple linear regression and multiple linear regression. Regression is a remarkably versatile statistical procedure that can be used not only to understand whether or not variables are related to each other (as in correlation) but also for providing estimates of the direction of the relationship and of the degree to which the variables are related. Beginning with a simple bivariate case analyzing a single predictor on a single outcome, the flexibility and ability for regression to analyze increasingly complex data, including binary outcomes, is discussed. Particular attention is paid to the ability of regression to be used to estimate the effect of a predictor on an outcome while statistically “controlling” for the values of other observed variables.

Extremal Dependence Modeling with Spatial and Survival Distributions

This paper investigates some properties of dependence of extreme values distributions both in survival and spatial context. Specifically, we prospose a spatial Extremal dependence coefficient for survival distributions. Madogram is characterized in bivariate case and multivariate survival function and the underlying hazard distributions are given in a risky context.