| A class of generalized normal distributions generated from the distribution of the beta random variable was developed. This generalized normal distribution has four parameters, which identify the location, scale and shape of the density function. The shape and moment properties of the generalized normal distribution were discussed. A region (based on the shape parameters) where the generalized normal distribution is bimodal was obtained. Closed form solutions for some first moments were obtained and upper bounds were established for all first moments. Estimation of parameters of the generalized normal distribution by the maximum likelihood method was discussed. It was also shown that the generalized normal distribution provides great flexibility in modeling symmetric heavy-tailed distributions, skewed and bimodal distributions. The flexibility of this distribution was illustrated by applying it to a variety of empirical data sets and comparing the results to previously used methods. |
