A FIRST ORDER LINEAR DIFFERENTIAL EQUATION APPROACH OF GENERATING CONTINUOUS PROBABILITY DISTRIBUTIONS REVIEW, ANALYSIS AND CHARACTERIZATIONS
By
Mohammad Shakil1 , Jai Narain Singh2 , Lishamol Tomy3 , R. C. Singh Chandel44, Tassaddaq Hussain5 , Aneeqa Khadim6, Mohammad Ahsanullah7 and B. M. G. Kibria8
1Department of Mathematics, Miami Dade College, Hialeah, Fl, USA-33012
2Department of Mathematics & Computer Science, Barry University, Miami Shores, Fl, USA-33168
3Department of Statistics, Deva Matha College, Kuravilangad, Kerala, India- 686633
4Department of Mathematics, D.V. Postgraduate College, Orai, Uttar Pradesh, India-285001
5,6Department of Statistics, Mirpur University of Science and Technology, Mirpur, Pakistan-10250
7Professor Emeritus, Rider University, NJ, USA-08648 8Department of Mathematics & Statistics, Florida International University, Miami, FL, USA- 33199
Email: mshakil@mdc.edu, jsingh@mail.barry.edu, lishatomy@gmail.com, rc chandel@yahoo.com, tafkho2000@gmail.com, aneeqa89@gmail.com, ahsan@rider.edu, kibriag@fiu.edu
(Received: September 16, 2024; In format: October 07, 2024; Revised: November 15, 2024; Accepted: November 20, 2024)
DOI: https://doi.org/10.58250/jnanabha.2024.54223
Abstract
Continuous probability distributions can be generated in many ways. To deal with various types of data or information, many researchers have developed flexible distributions. Since the pioneer work of Karl Pearson in 1895 and 1901, the first order linear differential equation approach of Pearson is a major milestone among different ways for generating univariate continuous probability distributions. In this paper, we present the first order linear differential equation approach for generating continuous probability distributions. A review of Pearson system of probability distributions is provided. We provide various new classes of the generalized Pearson system of probability distributions that could be generated using the first order linear differential equation approach. Some distributional properties and characterizations are also provided. It is observed that the first order linear differential equation approach is an elegant method for generating new families of univariate continuous probability distributions. Finally, we provide prospects of further research and directions in which future progress can be made.
2020 Mathematical Sciences Classification: : 62E10; 62E15.
Keywords: First order linear differential equation; Generalized Pearson distributions; Integrating factor; Partial fractions; Pearson distributions.