As mentioned in previous monographs (I, II, and III), in designing a stochastic model for a particular modeling problem, an investigator will be vitally interested to know if their model fits the requirements of a specific underlying probability distribution. To this end, the investigator will rely on the characterizations of the selected distribution. Generally speaking, the problem of characterizing a distribution is an important problem in various fields and has recently attracted the attention of many researchers. Consequently, various characterization results have been reported in the literature. These characterizations have been established in many different directions. The present work deals with the characterization of a 800 newly proposed univariate continuous distributions as they became available to the author rather than the order of their importance. This work is a continuation of our previous works (Hamedani and Safavimanesh, 2017), (Hamedani, 2017), (Hamedani and Maadooliat, 2017), (Hamedani, 2018a), (Hamedani, 2018b), (Hamedani 2019) and (Hamedani 2021) on the characterizations of distributions introduced in 2019-2021. The current work and the previous published papers mentioned above may serve as a source of preventing the reinvention and/or duplication of the existing distributions in the future.

As mentioned in previous monographs (I, II, and III), in designing a stochastic model for a particular modeling problem, an investigator will be vitally interested to know if their model fits the requirements of a specific underlying probability distribution. To this end, the investigator will rely on the characterizations of the selected distribution. Generally speaking, the problem of characterizing a distribution is an important problem in various fields and has recently attracted the attention of many researchers. Consequently, various characterization results have been reported in the literature. These characterizations have been established in many different directions. The present work deals with the characterization of a 800 newly proposed univariate continuous distributions as they became available to the author rather than the order of their importance. This work is a continuation of our previous works (Hamedani and Safavimanesh, 2017), (Hamedani, 2017), (Hamedani and Maadooliat, 2017), (Hamedani, 2018a), (Hamedani, 2018b), (Hamedani 2019) and (Hamedani 2021) on the characterizations of distributions introduced in 2019-2021. The current work and the previous published papers mentioned above may serve as a source of preventing the reinvention and/or duplication of the existing distributions in the future.

As mentioned in previous monographs (I, II, and III), in designing a stochastic model for a particular modeling problem, an investigator will be vitally interested to know if their model fits the requirements of a specific underlying probability distribution. To this end, the investigator will rely on the characterizations of the selected distribution. Generally speaking, the problem of characterizing a distribution is an important problem in various fields and has recently attracted the attention of many researchers. Consequently, various characterization results have been reported in the literature. These characterizations have been established in many different directions. The present work deals with the characterization of a 800 newly proposed univariate continuous distributions as they became available to the author rather than the order of their importance. This work is a continuation of our previous works (Hamedani and Safavimanesh, 2017), (Hamedani, 2017), (Hamedani and Maadooliat, 2017), (Hamedani, 2018a), (Hamedani, 2018b), (Hamedani 2019) and (Hamedani 2021) on the characterizations of distributions introduced in 2019-2021. The current work and the previous published papers mentioned above may serve as a source of preventing the reinvention and/or duplication of the existing distributions in the future.