چكيده به لاتين
survival analysis is one of the topices of statistics that has application in various fields including computer sciences, insurance, economics, medicine, engineering, epidiomology and agricultural. The main problems in this thesis are to define and find suitable models for use as lifetime distributions and then inferences based on proposed models.
A widely used family of continuous distributions in lifetime data analysis is Burr distributions family. The main purpose of this thesis is to define new families of Burr distributions and generalizations of some types of Burr distributions to describe and fit the data sets with non-monotonic hazard rates, such as the U-shaped, unimodal, unimodal-increasing and bath-tub-decreasing hazard rates. For each prposed distribution in this thesis, choose a better method for estimation its parameters is another of our challenges. Various methods for estimation parameters ( maximum likelihood, modifications of maximum likelihood, bayesian analysis, estimation based on the principle of maximum entropy and kullback-leibler divergence of survival functions) are used.
it is important to note that, although in nature most of the lifetime values are continuous, but because of the difficulty of sampling a continuous distribution, the observed values are often discrete. Hence, there is a basic request to discrete lifetime distributions in survival analysis. To meet this request , discretization of widely-used continuous lifetime distributions is helpful to increase the accuracy and understand lifetime data generated of these models. Therefore another goal of this thesis is to define new discretization methods and also discretization new continuous lifetime distributions defined because of the impotance and application discrete lifetime distributions in survival analysis.
