Uniform Distribution Of The Relevant Properties And Testing

With the rapid development of society, it is a trend in recent years to use mathematical methods quantitatively to analyze the problems. Quantitative analysis will make the research conclusions more credible. In probability and statistics, uniform distribution is one of the commonly-used distributions, and it plays an important role in practice. It is widely used in the fields of genetics, biology, finance, transportation and so on. Therefore, the research of the uniform distribution attracts the interest of a large number of scholars.This dissertation is organized as following:The first chapter introduces the background of our research of uniform distribution, random number and hypothesis test. The importance of the research on uniform distribution is illustrated, then we introduce the main research of this dissertation.The second chapter firstly deals with the relationships between the uniform distribution and the common continuous distributions, highlights the relationships between the uniform distribution and χ2 distribution, t distribution, F distribution in statistics. Then the concepts and properties of minimum risk equivalent estimator (MREE) are introduced. At the same time, the parameter estimators and asymptotic properties of three kinds of different uniform distribution are researched. Simulation examples are illustrated that our results are available.The third chapter firstly covers the definition and related theorem of random number, and generation of random numbers for the standard uniform distribution. Then we introduce the generation of random numbers for non-uniformly continuous distributions, including normal distribution and exponential distribution, and use examples to illustrate the generation methods of random numbers.The hypothesis tests of uniform distributions are conducted in the fourth chapter. Firstly, we introduce the concept of goodness of fit test and its related properties in detail. Then the P-P and Q-Q plots test are introduced, meanwhile Kolmogorov-Smirnor (KS) test and Pearson chi-square goodness of fit tests are introduced by illustrated numerical examples.The Final chapter gives a summary for this dissertation, and further research.