Master's degree in Statistics, Shiraz University, Iran
Abstract
The main role in bell-shaped graphs is played by the normal distribution, but researchers are always interested in constructing distributions similar to the normal distribution. For this purpose, flexible distributions have been introduced as an alternative to the normal distribution. This article introduces some of these distributions. First, the slash distribution, which is a family of mixed distributions of normal scale, is introduced. This distribution has a heavier tail than the normal distribution, and this feature makes the slash distribution a suitable alternative to the normal distribution. Then, the Chule slash distribution is introduced. Next, the new modified slash distribution is introduced, and then the modified Chule slash distribution is explained. Some of the properties of these distributions, such as random representation, density function, and moments, are also examined. An example is provided to further explain the material.