Farlie–Gumbel–Morgenstern Bivariate Moment Exponential Distribution and Its Inferences Based on Concomitants of Order Statistics

Sasikumar Padmini Arun, Christophe Chesneau (), Radhakumari Maya and Muhammed Rasheed Irshad
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Sasikumar Padmini Arun: Kerala University Library, Research Centre, University of Kerala, Trivandrum 695 034, India
Christophe Chesneau: Department of Mathematics, Université de Caen Basse-Normandie, 14032 Caen, France
Radhakumari Maya: Department of Statistics, University College, Trivandrum 695 034, India
Muhammed Rasheed Irshad: Department of Statistics, Cochin University of Science and Technology, Cochin 682 022, India

Stats, 2023, vol. 6, issue 1, 1-15

Abstract: In this research, we design the Farlie–Gumbel–Morgenstern bivariate moment exponential distribution, a bivariate analogue of the moment exponential distribution, using the Farlie–Gumbel–Morgenstern approach. With the analysis of real-life data, the competitiveness of the Farlie–Gumbel–Morgenstern bivariate moment exponential distribution in comparison with the other Farlie–Gumbel–Morgenstern distributions is discussed. Based on the Farlie–Gumbel–Morgenstern bivariate moment exponential distribution, we develop the distribution theory of concomitants of order statistics and derive the best linear unbiased estimator of the parameter associated with the variable of primary interest (study variable). Evaluations are also conducted regarding the efficiency comparison of the best linear unbiased estimator relative to the respective unbiased estimator. Additionally, empirical illustrations of the best linear unbiased estimator with respect to the unbiased estimator are performed.

Keywords: concomitants of order statistics; moment exponential distribution; inference (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2023
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