The Area Biased Amarendra Distribution with its Application to Model Lifetime Data
M. Ahajeeth
, Maryam Mohiuddin
, R. Kannan
Abstract
In this paper, we introduce a new generalization of Amarendra distribution and the model is referred to as Area Biased Amarendra distribution. The statistical properties of the new model are derived.The model parameters are estimated by the method of maximum likelihood estimation. The simulation study is conducted to know the flexibility of the parameter of the model. Two real-life data sets are presented and examined to validate the applicability of the model.
References
1. A. Para; T.R. Jan; On Three Parameter Weighted Pareto Type II Distribution: Properties and Applications in Medical Sciences, Applied Mathematics and Information Sciences Letters, 6(1) 13-26 (2018).
2. A. Rather; C. Subramanian; Characterization and Estimation of Length Biased Weighted Generalized Uniform Distribution, International Journal of Scientific Research in mathematical and Statistical sciences, 5(5) 72-76 (2018).
3. A. Rather; C. Subramanian; On Weighted Sushila Distribution with Properties and its Applications, International Journal of Scientific Research in Mathematical and Statistical Sciences, 6(1) 105-117 (2019).
4. E. Bonferroni; Elmenti di statistic a generale, Libreria Seber, Firen, (1930).
5. J. Lappi; R. L. Bailey; Estimation Of Diameter Increment Function or Other Tree Relations Using Angle-
Count Samples, Forest Science, 33 725-739 (1987).
6. M. G. Badar; A. M Priest; Statistical Aspects of Fiber and Bundle Strength in Hybrid Composites,
Progress in Science and Engineering Composites, Hayashi, T., Kawata, K. and Umekawa, S. (eds.),
ICCM-IV, Tokyo, 1129-1136 (1982).
7. M. O. Lorenz; Methods of Measuring the Concentration of Wealth, American Statistical Association, 9
209–219 (1997).
8. M. Zelen; Problems in Cell Kinetic and the Early Detection of Disease, in Reliability and Biometry, F. Proschan; and R. J. Sering; eds., SIAM, Philadelphia, 701-706 (1974).
9. Maryam Mohiuddin; Shabir A. Dar; Arshad A. Khan; A. A. Rather; R. Kannan; A Generalization of Devya distributin with Application to real-life data, International Journal of Statistics Reliability and Engineering, 7(3) 313-325 (2020).
10. Maryam Mohiuddin; Shabir A. Dar; Arshad A. Khan; M. Ahajeeth; On Weighted Nwikpe distributin: Properties and Applications, Information Science Letters, 11(1) 85-96 (2022)
11. P. C. Van Deusen; Fitting Assumed Distributions to Horizontal Point Sample Diameters, Forest Science,
32 146-148 (1986).
12. R. A. Fisher; The Effects of Methods of Ascertainment upon the Estimation of Frequencies, Annals of
Eugenics, 6 13-25 (1934).
13. R. Cox; Some sampling problems in technology, In New Development in Survey Sampling, Johnson, N.
L. and Smith, H, Jr. (eds.) New York Wiley Inter science, 506-527 (1969).
14. R. Rao; On Discrete Distributions Arising out of Method of Ascertainment, in Classical and Contagious
Discrete, G.P. Patiled; Pergamum Press and Statistical publishing Society, Calcutta, 320-332 (1965).
15. R. Shanker; Amarendra Distribution and ItsApplications, American Journal of Mathematics and Statistics,
6(1) 44-56 (2016).
16. Rényi; On Measures of Entropy and Information, Proceedings of fourth Berkeley Symposium Mathematics Statistics and Probability, University of California Press, Berkeley, Vol 1 547–561 (1961).
17. Tsallis; Possible Generalization of Boltzmann-Gibbs Statistics, Journal of Statistical Physics, 5252 479- 487 (1988).