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چکیده
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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
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