ON CHARACTERIZATION OF 2KTH ORDER WEIGHTED MAXWELL BOLTZMANN DISTRIBUTION

Characterizing a probability distribution is essential in the fields of probability and statistics. This paper presents the characterization results of the 2Kth order weighted Maxwell Boltzmann distribution (KWMBD). The characterization results are based on the coefficient of variance, a straightforward relationship between two truncated moments, the conditional expectation of a specific function of the random variable, the hazard function, and the reverse hazard function. Notably, for these characterizations, the cumulative distribution function (CDF) does not need to have a closed form; instead, the CDF is derived from the solution of a first-order differential equation. This approach not only extends the applicability of the KWMBD but also establishes a crucial link between probability theory and differential equations. The resulting insights have significant implications for both theoretical research and practical applications in statistical modeling and analysis.