Parametric Extensions of the Exponential Distribution
The exponential distribution has a single parameter that serves both as a scale and as a frailty parameter. Moreover, if an age parameter or a Laplace transform parameter is introduced, the distribution remains an exponential distribution and only the parameter is changed. This means that of the various parameters discussed in Chapter 7, only power, convolution, moment, tilt, and resilience can be used to generate two parameter extensions of the exponential distribution. It is shown below that the introduction of moment and convolution parameters both lead to the gamma family, and consequently only four of these extensions are distinct. These four extensions with two parameters are discussed in this chapter along with their further extensions to three-parameter families.
KeywordsExponential Distribution Gamma Distribution Hazard Rate Survival Function Weibull Distribution
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