چكيده به لاتين
Abstract:
This thesis discusses the dynamic and weighted Renyi’s entropy. The dynamic and weighted entropies
have many applications in various fileds of science that some of them are mentioned in this
thesis. This thesis consists of 4 chapters. The first chapter express introductions and required backgrounds
for entry into next chapters. Also, in this chapter, a new distribution that generates many
lifetime distributions and therefore used in the examples of next chapters.
The scond chapter introduces the weighted Renyi’s entropy in lifetime distributions. This chapter
introduces three types of weighted entropies that is weighted Renyi’s entropy of order , weighted
residual Renyi’s entropy of order and weighted past Renyi’s entropy of order . After introducing
them, we illustrate their properties.
The thired chpter consists of dynamic and cumulative Renyi’s entroy of order . In this chapter,
at first, we investigate the properties of cumulative past Renyi’s entropy of order then introduce
weighted cumulative past Renyi’s entropy of order . Properties of this entropy and relations with
other entropies including inequalities, non-parametric classes, linear transformations and so on to
be expressed. At the end, with practical examples, illustrate the importance of these entropies.
In chapter 4, after introducing interval Renyi’s entropy, we consider properties and some orders
based on this entropy. Finally, a numerical result applied to present our work for SLCW distribution.
Keywords: Renyi’s entropy, cumulative entropy, weighted entropy, distribution function
