Mahmoud Afshari

In order to have more flexibility in the shape of the distribution to interpret and explain real data, constructing more appropriate statistical distributions has been a topic of interest to researchers in recent decades. Classical statistical distributions, although efficient in many cases, may be inadequate when dealing with data that has complexities such as skewness and multimodality. The family of new distributions introduced in recent years has more flexibility for fitting data, which leads to better models for existing data. In this thesis, a mathematical model for logistic distributions with three different modes is investigated and developed. These types of distributions are used in many statistical and engineering problems such as complex and nonparametric data analysis. Also, the properties and characteristics of these distributions, including the probability density function, the cumulative distribution function, and parameter estimation methods, are investigated. Finally, with the help of simulation, practical applications and advantages of using this distribution in practice compared to other common models have been investigated. The results of this research can be useful in improving decision-making processes and analyzing complex data.