We present an algorithm to determine the set of essential singular solutions of a differential equation. Essential singular solutions can be informally described as follows: the general solution of a differential equation is usually described as a solution depending on a number of arbitrary constants equal to the order of the differential equation. The essential singular solutions are those tha...

In this paper we wish to establish the integral representations of generalized relative type and generalized relative weak type as introduced by Datta et al [9]. We also investigate their equivalence relation under some certain conditions.

In this paper we consider three parameter generalized exponential distribution. Exact expressions and some recurrence relations for single and product moments of lower generalized order statistics are derived. Further the results are deduced for moments of order statistics and lower records and characterization of this distribution has been considered on using the conditional moment of the lowe...

The dual generalized order statistics is a unified model which contains the well known decreasingly ordered random data such as (reversed ordered) order statistics and lower record values. In the present paper, some characterization results on the power function distribution based on the properties of dual generalized order statistics are provided. The results are proved without any rest...