Document Type

Article

Language

eng

Format of Original

3 p.

Publication Date

2014

Publisher

Chungcheong Mathematical Society

Source Publication

Journal of the Chungcheong Mathematical Society

Source ISSN

1226-3524

Original Item ID

doi: 10.14403/jcms.2014.27.3.475

Abstract

Lee and Lim (2009) state three characterizations of Loamax, exponential and power function distributions, the proofs of which, are based on the solutions of certain second order non-linear differential equations. For these characterizations, they make the following statement : "Therefore there exists a unique solution of the differential equation that satisfies the given initial conditions". Although the general solution of their first differential equation is easily obtainable, they do not obtain the general solutions of the other two differential equations to ensure their claim via initial conditions. In this very short report, we present the general solutions of these equations and show that the particular solutions satisfying the initial conditions are uniquely determined to be Lomax, exponential and power function distributions respectively.

Comments

Published version. Journal of the Chungcheong Mathematical Society, Vol. 27, No. 3 (2014): 475-477. DOI. © 2014 Chungcheong Mathematical Society.

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