Η κατανομή Lindley και οι εφαρμογές της στον αναλογισμό
The Lindley distribution and its application in actuarial science
Ταχλιαμπούρης, Κωνσταντίνος - Παναγιώτης
The Diploma Thesis that will follow, we will examine the Lindley Distribution and variations of it. The Lindley Distribution was introduced by Lindley (1958, 1965) and belongs to the Exponential Distributions family. In Chapter 1, we will get acquainted with the simple form of the Distribution (Density function, etc.) while compared to the Exponential Distribution with regard to the assessment of the θ parameter but also adapting the Distribution to data. The results clearly indicate Lindley’s better adaptation against the Exponential Distribution. In Chapter 2, the competing risks life time data model is examined applied in the Actuarial science. Without excluding generality, we shall observe the Lindley Distribution behavior with 2 causes of competing failures and we shall attempt to evaluate said parameters. In Chapter 3, we will examine the form and parameters of the Generalized Lindley Distribution with three parameters (GL), which presents more flexibility than Lindley(θ) (Zakerzadeh (2009)). Special cases of the GL is the Exponential and the Gamma Distributions. Through an algorithm of random samples production, we shall examine two examples with different Data in which GL has better application than Gamma, Weibull and Lognormal Distributions. In conclusion Chapter 4 presents a new Generalized Poisson-Lindley Distribution, which derives from the Poisson Distribution when the λ parameter follows the Lindley Distribution with two parameters which we symbolize as TPLD(θ,a) (Shanker (2013)). The need for the creation of such model derives from the Insurance Market and the Premium rates calculation, where a Distribution referencing potential Liability is adopted which can be verified or not. Specifically, except from minimizing the deviation from the actual Data, this new Distribution can describe the extreme values («heavy tail») (Shanker (2013)). Reference is made to the allocation Distribution and its general characteristics such as shape, skewness and kyrtosis while a comparison is made with other Distributions as per their application. The results show the better adaptation of the NGPL(θ,a) in comparison to other widely used Distributions in the Actuarial Science.