A New Extended Geometric Distribution: Properties, Regression Model, and Actuarial Applications

Mohammed Mohammed Ahmed Almazah, Tenzile Erbayram, Yunus Akdoğan, Mashail M. AL Sobhi and Ahmed Z. Afify
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Mohammed Mohammed Ahmed Almazah: Department of Mathematics, College of Sciences and Arts (Muhyil), King Khalid University, Muhyil 61421, Saudi Arabia
Tenzile Erbayram: Department of Statistics, Faculty of Science, Selçuk University, 42250 Konya, Turkey
Yunus Akdoğan: Department of Statistics, Faculty of Science, Selçuk University, 42250 Konya, Turkey
Mashail M. AL Sobhi: Department of Mathematics, Umm-Al-Qura University, Makkah 24227, Saudi Arabia
Ahmed Z. Afify: Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt

Mathematics, 2021, vol. 9, issue 12, 1-16

Abstract: In this paper, a new modified version of geometric distribution is proposed. The newly introduced model is called transmuted record type geometric (TRTG) distribution. TRTG distribution is a good alternative to the negative binomial, Poisson and geometric distributions in modeling real data encountered in several applied fields. The main statistical properties of the new distribution were obtained. We determined the measures of value at risk and tail value at risk for the TRTG distribution. These measures are important quantities in actuarial sciences for portfolio optimization under uncertainty. The TRTG parameters were estimated via maximum likelihood, moments, proportions, and Bayesian estimation methods, and the simulation results were determined to explore their performance. Furthermore, a new count regression model based on the TRTG distribution was proposed. Four real data applications were adopted to illustrate the applicability of the TRTG distribution and its count regression model. These applications showed empirically that the TRTG distribution outperforms some important discrete models such as the negative binomial, transmuted geometric, discrete Burr, discrete Chen, geometric, and Poisson distributions.

Keywords: geometric distribution; insurance data; Bayesian estimation; Monte Carlo simulation; stochastic ordering; value at risk; count regression (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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