W. T. Wells

Bio: W. T. Wells is an academic researcher. The author has contributed to research in topics: Extreme value theory & Weibull distribution. The author has an hindex of 1, co-authored 1 publications receiving 109 citations.

On the Possibility of Improving the Mean Useful Life of Items by Eliminating Those with Short Lives

Abstract: When everything possible has been done to produce articles with long lives, there remains the possibility that a further improvement in the articles may be obtained by running them, for some time, under realistic conditions. The fraction that does not fail may have a longer mean remaining life than the original articles. In this paper conditions on the life distribution of the original articles are found which will insure this. The Weibull, gamma, exponential, extreme value and log-normal life distributions are examined in detail. The most interesting case is the log-normal, for which it is always possible to increase the mean life to any extent desired by continuing to test until a sufficiently large number of articles have failed.

Statistical Size Distributions in Economics and Actuarial Sciences

Abstract: A comprehensive account of economic size distributions around the world and throughout the years In the course of the past 100 years, economists and applied statisticians have developed a remarkably diverse variety of income distribution models, yet no single resource convincingly accounts for all of these models, analyzing their strengths and weaknesses, similarities and differences. Statistical Size Distributions in Economics and Actuarial Sciences is the first collection to systematically investigate a wide variety of parametric models that deal with income, wealth, and related notions. Christian Kleiber and Samuel Kotz survey, compliment, compare, and unify all of the disparate models of income distribution, highlighting at times a lack of coordination between them that can result in unnecessary duplication. Considering models from eight languages and all continents, the authors discuss the social and economic implications of each as well as distributions of size of loss in actuarial applications. Specific models covered include: Pareto distributions Lognormal distributions Gamma-type size distributions Beta-type size distributions Miscellaneous size distributions Three appendices provide brief biographies of some of the leading players along with the basic properties of each of the distributions. Actuaries, economists, market researchers, social scientists, and physicists interested in econophysics will find Statistical Size Distributions in Economics and Actuarial Sciences to be a truly one-of-a-kind addition to the professional literature.

The Inverse Gaussian Distribution as a Lifetime Model

Abstract: Early occurrence of certain events such as failure or repairs is a common phenomenon in the lifetime of industrial products. Often, the log normal distribution has been found as a useful model to be applicable whenever the early occurrences dominate a lifetime distribution. In this paper we suggest the use of the inverse Gaussian distribution for a model of such lifetime behavior and discuss different reliability features of the distribution. It is shown that its failure rate is nonmonotonic, initially increasing and then decreasing. Advantages in the use of the inverse Gaussian over the log normal are given. Certain numerical results are presented for illustration.