الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
order statistics (OSs) and record values are very useful concepts in statistics. Since they have a wide range of applications, for example, industrial applications like life testing, economic applications like finance, insurance and auction and military applications like radar target recognition and missile appraisal. Also, OSs are among the most fundamental tools in mathematical statistics, like non-parametric statistics and statistical inference.The limit theorems are one of the most important branches of OSs, since they play an important role in all applications of OSs. One of these theorems is the Extreme Value Theory, which simplifies many statistical models in various practical fields, like in industry for quality control purposes and in marketing as lists of best sales, in addition to meteorology, seismology, traffic jams at peak times, the maximum load of a concrete structure or an electric station, and the problems caused by floods and drought.It is known that the mixture model, which is a convex combination of two distributions, is a powerful and flexible tool for modelling complex data by combining the properties of the individual distributions. Besides this advantage, mixture models have been used in many applications in statistical analysis and machine learning, such as modelling, clustering, classification, latent class, and survival analysis.