Further Study Of The Three Most Important Distribution And Its Nature

Chi-square distribution, t distribution and F distribution, who come from thestandard normal distribution, are the three basic distribution of probability theory andmathematical statistics. As a data analysis model, statistical probability distributioncan be said as the cornerstone of statistics because of the amount of applications inany distribution model. People often need to know its distribution when they usingstatistics in statistical inference. When the overall distribution function is known, thesampling distribution is determined, however, it is difficult to find out a precisedistribution of statistics in general. So people often achieve analyzing and forecastingwith the help of known distribution. So it is necessary to analysis commonly used inresearch of the distribution of the three most important statistics. Introducing threedistributions, many scholars have just given directly density function, expectation andvariance of the distribution, but they have not focused on derivation of the densityfunction and the digital signature. so that the learning process is simply a memory,and a deep understanding of its meaning cannot been get more in-depth understandingof the theory a probability theory and mathematical statistics.In order to betterunderstand the value and significance of the sampling distribution, the mostimportant of the three further analysis of the distribution, respectively, using thedistribution function method, the characteristic function method, multi-dimensionalball transform method to get probability density function is derived more specific, andthe chi-square distribution, t distribution and F distribution’s nature of the densitydistribution function, and its distribution consistent asymptotic normality doneintensive research, the distribution itself from moment analysis extended to thefamily of the corresponding distribution of the moments, layers of depth, made witha certain originality of views and ideas, so that the distribution of the three morecomplete theory has important significance.