SOME INFERENCES ON CHARACTERIZATIONS OF PROBABILITY DISTRIBUTIONS, WITH SPECIAL REFERENCE TO THE CONTRIBUTIONS OF PROFESSOR C. R. RAO ON THE CHARACTERIZATIONS OF DISTRIBUTIONS
By
M. Ahsanullah1, M. Shakil2 and R. C. Singh Chandel3
1Professor Emeritus, Rider University, Lawrenceville, NJ, USA-08648 2Miami Dade College, Hialeah, FL, USA-33012 3Department of Mathematics, D.V. Postgraduate College, Orai, Uttar Pradesh, India - 285001
Email: ahsan@rider.edu, mshakil@mdc.edu, rc_chandel@yahoo.com
(Received: March 25, 2026; In format: April 13, 2026; Revised: June 25, 2026; Accepted: June 30, 2026)
DOI: https://doi.org/10.58250/jnanabha.2026.56119
Abstract
The characterization of probability distributions plays a fundamental role in statistical theory and mathematical statistics. Before applying any probabilistic model to observed data, it is essential to ensure that the assumed distribution satisfies the relevant defining properties. Characterization theorems provide powerful tools for identifying probability distributions through functional, moment-based, or distributional properties of random variables. In this paper, we present several important characterization results for classical probability distributions, with special reference to the contributions of Professor C. R. Rao on the characterization of distributions. We also propose and develop some new characterization results for logistic distribution. Logistic distribution occupies an important place in statistical theory and is often regarded as a close analogue of normal distribution. It arises naturally in several theoretical and applied contexts, including logistic growth models and logistic regression. The present work discusses basic properties and selected characterizations of the logistic distribution, thereby contributing to the existing literature on characterization theory.
2020 Mathematical Sciences Classification: 60E05; 62E10; 62E15; 62G30.
Keywords and Phrases: Characterization; characteristic function; logistic distribution; moments; statistical inference.