Relationships among continuous probability distributions and some applications

• Main Authors: De Los Santos, Dante M., Andres, Marian Rochelle Leovigilda V.
• Format: text
• Language: English
• Published: Animo Repository 1998
• Subjects: Probabilities; Distribution (Probability theory); Functions, Continuous
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16500
• Institution: De La Salle University

Students taking up statistics courses are introduced to various probability distributions. Although probability distributions can be derived from other probability distributions, common univariate distributions are usually discussed separately in introductory probability textbooks. The purpose of this paper is to present, for some continuous univariate distributions, a way of relating these distributions with one another. This paper is actually an exposition of the article written by Lawrence M. Leemis, entitled Relationships Among Common Univariate Distributions. In this article, a diagram was drawn to show the relationships between particular distributions. The researchers proved the relationships stated in the article. The said proofs are contained in this paper. However, the researchers did this for the continuous case only. The researchers were able to prove thirty-one relationships using the transformation technique and the moment generating function technique. In addition, some applications were discussed.