A Graphical Method to Assess Goodness-of-Fit for Inverse Gaussian Distribution

A Q-Q plot is an effective and convenient graphical method to assess a distributional assumption of data. The primary step in the construction of a Q-Q plot is to obtain a closed-form expression to represent the relation between observed quantiles and theoretical quantiles to be plotted in order that the points fall near the line y = a + bx. In this paper, we introduce a Q-Q plot to assess goodness-of-fit for inverse Gaussian distribution. The procedure is based on the distributional result that a transformed random variable Y = vertical bar root lambda(X - mu) / mu root X vertical bar follows a half-normal distribution with mean 0 and variance 1 when a random variable X has an inverse Gaussian distribution with location parameter mu and scale parameter lambda. Simulations are performed to provide a guideline to interpret the pattern of points on the proposed inverse Gaussian Q-Q plot. An illustrative example is provided to show the usefulness of the inverse Gaussian Q-Q plot.