Chapter 4 Truncated Distributions

Chapter 4. Truncated Distributions This Chapter presents a simulation study of several of the con dence intervals rst presented in Chapter 2. Theorem on p. 50 shows that the ( , ). trimmed mean Tn is estimating a parameter T with an asymptotic variance 2. equal to W /( )2 . The rst ve sections of this Chapter provide the theory needed to compare the di erent con dence intervals. Many of these results will also be useful for comparing multiple linear regression estimators. Mixture Distributions are often used as outlier models. The following two de nitions and proposition are useful for nding the mean and variance of a mixture distribution. Parts a) and b) of Proposition below show that the de nition of expectation given in De nition is the same as the usual de nition for expectation if Y is a discrete or continuous random variable. Definition The distribution of a random variable Y is a mixture distribution if the cdf of Y has the form.

Chapter 4 Truncated Distributions This chapterpresentsa simulationstudy of several of the confidence intervals first presented in Chapter 2. Theorem 2.2 on p. 50 shows that the (α,β) trimmed mean Tn is estimating a parameterμT with an asymptotic variance equal toσ2 W /(β−α)2.The firstfive sectionsof thischapterprovide the theory

Loading..

Tags:

  Chapter

Information

Related search queries