ABSTRACT
The standard or canonical form of the two-parameter inverse Gaussian distribution has the probability density function. From the standard two-parameter form of the inverse Gaussian distribution, a three-parameter inverse Gaussian distribution can be proposed easily by introducing a threshold parameter, ?. The standardized inverse Gaussian distribution, unlike the gamma and the Weibull distributions, does not become reverse J-shaped and retains the bell shape with a discernible mode for all values of the shape parameter k. In this respect, it resembles the lognormal distribution more than either the Weibull or the gamma distributions. When the shape parameter k is small the standardized inverse Gaussian density function is very close to the standard normal density function. As the shape parameter k gets large the standardized inverse Gaussian density function becomes highly skewed and is significantly different from the standard normal density function.
