Prof. Rama Shanker
Department of Statistics, Assam University, Silchar, Assam, India
Title: ON COMPOUNDING OF CONTINUOUS DISTRIBUTIONS WITH THEIR PROPERTIES AND APPLICATIONS
Abstract:
The present era of distribution theory stresses on
solving problems faced by practitioners and applied researchers and proposes a
variety of probability distributions so that the nature of lifetime data can be
better assesses and investigated from different fields of knowledge. It has
been observed that there is a strong need for introducing useful probability
distributions for better exploration of the real-life phenomenon. During recent
decade, trends and practices for proposing probability distributions have
totally taken a new paradigm.
The present interdisciplinary research focuses on
medical sciences, engineering and finance and it is not easy to assess the
nature of the data in these fields due to the structural properties of the
distributions and the stochastic nature of the data. For example, the
search for a suitable probability distributions for the survival analysis of
cancer patients are really challenging because survival times of cancer
patients are stochastic in nature and are highly positively skewed. The
classical well-known one parameter and two-parameter probability distributions
rarely provide better fit to survival times of cancer patients. It has been
observed that the compounding of positively skewed distributions results into a
highly positively skewed distributions and are suitable probability models for
highly positively skewed data from biomedical sciences and engineering.
In
this paper, the compounding of (i) gamma distribution and Shanker distribution
and (ii) gamma distribution and Sujatha distribution has been discussed for the
modeling of survival times of cancer patients. Some important properties of these
compound distributions have been discussed. Method of maximum likelihood has
been used to estimate the parameters. A simulation study has been conducted to
know the consistency of maximum likelihood estimators. Two real datasets, one
relating to acute bone cancer and the other relating to head and neck cancer,
has been considered to examine the applicability, suitability and flexibility
of these compound distributions. The goodness of fit of these compound distributions
shows quite satisfactory fit over other considered distributions
Keywords: Compounding, Inverse moments, Hazard
function, Reversed hazard function, Stress-strength Parameter, maximum
likelihood estimation, Applications.
Biography:
Dr. Rama Shanker has completed his Bachelor,
Master and Ph.D in Statistics from Department of Statistics, Patna University,
Patna, India. He obtained his Ph.D degree on the Topic: “On Generalized
Logarithmic Series Distributions and Their Applications” in 2003. He has worked as Assistant Professor of
Statistics at the College of Business and Economics, Eritrea from April, 2006
to April, 2012, as associate Professor at the College of Science, Eritrea
Institute of Technology, Eritrea from October, 2012 to July, 2014 and as a
Professor and Head of Department of Statistics from August 2014 to July 2018. He
was the founding Editor in chief of the Eritrean Journal of Science and
engineering, a biannual journal published from Eritrea Institute of Technology,
Eritrea. On 31st October, 2019, he joined as Associate Professor of
Statistics, Department of Statistics, Assam University, Silchar and since 10th May, 2024, he is working as Professor, Department of Statistics, Assam
University, Silchar, Assam. He has authored one standard text book titled,
“Introduction to Calculus for Business and Economics” published from GRD
Prakashan, New Delhi. His research interests include Distribution Theory,
Modeling of Lifetime Data, Statistical Inference, Linear Programming problem,
Transportation and Assignment Problems. He has 227 research papers published in
national and international journals of Statistics, Biostatistics, Mathematics
and Operations research. Two students have awarded Ph.D degree under his
supervision and five students are working under his supervision for their Ph.D
degrees. He has been working as Associate editors and editorial board members
of several international journals.