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Recently, a generalization of the Pearson differential equation has appeared in the literature, from which a vast majority of continuous probability density functions (pdf’s) can be generated, known as the generalized Pearson system of continuous probability distributions. This paper derives a new family of distributions based on the generalized Pearson differential equation, which is a natural generalization of the generalized inverse Gaussian distribution. Some characteristics of the new distribution are obtained. Plots for the cumulative distribution function, pdf and hazard function, tables with percentiles and with values of skewness and kurtosis are provided. It is observed that the new distribution is skewed to the right and bears most of the properties of skewed distributions. As a motivation, the statistical applications of the results to a problem of forestry have been provided. It is found that our newly proposed model fits better than gamma, log-normal and inverse Gaussian distributions. Since many researchers have studied the use of the generalized inverse Gaussian distributions in the fields of biomedicine, demography, environmental and ecological sciences, finance, lifetime data, reliability theory, traffic data, etc., we hope the findings of the paper will be useful for the practitioners in various fields of theoretical and applied sciences.

A New Family of Distributions Based on the Generalized Pearson Differential Equation with Some Applications