A class of beta-exponential distributions: Properties, estimation and applications

Researchers in statistics are sometimes faced with situations in which a suitable model to fit an observed data set is not readily apparent. Thus it is often necessary to use a general model that is likely to include a model suitable for the data as a special case. In this dissertation a new general model, a class of beta-exponential distributions, generated from the distribution of the beta random variable, is developed. The beta-exponential distribution is a three parameter probability model. The parameters identify the shape and scale of the density function. Properties such as moments and limiting properties are established. The method of moments and the maximum likelihood method are used to estimate the parameters. Some real life data are fitted and the goodness of fit is compared to that of the Weibull, the gamma, the exponentiated-exponential, the Lagrange gamma, and the beta-normal family. The hazard function of the beta-exponential distribution is investigated and compared to the hazard functions of the gamma, the Weibull, and the exponentiated-exponential distributions. Finally, a simulation study is conducted to investigate the properties of the maximum likelihood estimates of the parameters of the beta-exponential distribution. In five of the seven data sets considered, the beta-exponential distribution provided a better fit than one or more of the other distributions used for comparison. Furthermore, the hazard function of the beta-exponential distribution behaves similarly to, but more general than, the hazard function of the Weibull, gamma and exponentiated-exponential distributions.