A new distribution for fitting four moments and its applications to reliability analysis

The problem of constructing a probability density function (pdf) from four prescribed moments arises in many fields, including engineering. This problem may be addressed by the Pearson and Johnson systems of distribution, but systems are complicated to implement and have other drawbacks. This article presents a new unimodal distribution characterized by four parameters. This distribution has a rich flexibility in shape, nearly encompassing the entire skewness–kurtosis region permissible for unimodal densities. This versatility enables it to approximate many well known distributions, and moreover, it specializes to several important cases such as the normal and the lognormal. The density and cumulative distribution function have proper analytical forms, unlike, for example the generalized lambda distribution. Moreover, the parameters can be easily computed from the moments, thus obviating the need for tables. The proposed distribution is applied to fit several theoretical distributions, as well as actual datasets, with very favorable results. In addition, we demonstrate the effectiveness of the distribution in an assortment of engineering problems, including nonlinear ocean waves, non-Gaussian stochastic processes, moment-based reliability analysis, and fatigue damage uncertainty prediction.