فضل الله لک

Records in a series of observations are quantities which are smaller or bigger than their preceding observations. The serial number in which a record occurred is known as record time. Statistical study of records started by Chandler (1952) for the first time. So far, lots of articles have been published in this field and record theory and record statistics have been examined in different aspects. Records play considerable role in issues such as fragments lifelong test, tolerance of constructional materials test, reliability of a system’s credit, quality control, and operations Research. In addition, analysis of meteorological, seismographic, sport events, and genetic data by records has shown acceptable results and has provided a favorable conditions for the future prediction. This thesis is organized as follows.In the first chapter of this thesis, basic concepts of records and its distribution and theorems is introduced.Chapter two proposes an algorithm to quickly generate samples of record values.In this chapter fisher information of generalized exponential distribution is ckecked. In the third chapter, records are studied in two-parameter exponential distribution and statistical inferences is made according to records. In chapter four we consider the likelihood and Bayesian estimation of the stress-strength reliability based on lower record values from the generalized exponential distribution.The estimators are derived and their properties are studied. Finally in chapter 5 Bayes and empirical Bayes estimate is derived for the parameter of the exponential model based on record statistics. The estimate is obtained using the squared error loss and linear-exponential (LINEX) loss functions. Empirical Bayes prediction bounds for future record values are also obtained. A numerical example is