Template:Confidence Bounds

Confidence Bounds
In this section, we present the methods used in the application to estimate the different types of confidence bounds for exponentially distributed data. The complete derivations were presented in detail (for a general function) in Chapter 5. At this time we should point out that exact confidence bounds for the exponential distribution have been derived, and exist in a closed form, utilizing the $${{\chi }^{2}}$$ distribution. These are described in detail in Kececioglu [20], and are covered in the section on test design in Chapter 11. For most exponential data analyses, Weibull++ will use the approximate confidence bounds, provided from the Fisher information matrix or the likelihood ratio, in order to stay consistent with all of the other available distributions in the application. The $${{\chi }^{2}}$$ confidence bounds for the exponential distribution are discussed in more detail in Chapter 11.