REMARKS ON A PAPER OF LEE AND LIM

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 di？？erential equations. For these characterizations, they make the following statement : \Therefore there exists a unique solution of the di？？erential equation that satis¯es the given initial conditions . Although the general solution of their ¯rst di？？erential equation is easily obtainable, they do not obtain the general solutions of the other two di？？erential equations to ensure their claim via initial con- ditions. 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, expo- nential and power function distributions respectively.