Length Biased Exp-Gamma Distribution and Its Applications
N. W. Andure (Yawale), N. R. Bhandale, R. B. Ade
Abstract
In this paper, a new distribution namely Length Biased Exp-Gamma distribution is proposed. The different
mathematical and statistical properties of the proposed distribution are derived. The survival function, hazard rate
function and mean residual life function of the proposed distribution are discussed. The expression for Bonferroni
and Lorenz curve of the proposed distribution is derived. The parameters of the proposed distribution are estimated
by using method of maximum likelihood estimation. Performance of the proposed model is tested using real life
data sets
References
1. A.I. Al-Omari and A. Al-Nasser and and E. Ciavolino; A Size-biased Ishita Distribution and Application to
Real Data. Quality & Quantity, 53(1), 493-512 (2019).
2. Ayesha; Size Biased Lindley Distribution and Its Properties a Special Case of Weighted Distribution.
Applied Mathematics, 8(6), 808-819 (2017).
3. C. Subramanian and A.A. Rather; A New Extension of Shanker Distribution with Real Life Data. Journal of
Xi’an University of Architecture & Technology, 12(3), 2001-2009 (2020).
4. C. Tsallis; Possible Generalization of Boltzmann-Gibb’s Statistics. Journal of Statistical Physics, 52(1-2),
479-487 (1988).
5. C.R. Rao; On Discrete Distributions Arising Out of Methods of Ascertainment. Sankhyā: The Indian Journal
of Statistics, Series A (1961-2002), 27(2/4), 311-324 (1965).
6. D.R. Cox; Some Sampling Problems in Technology. In New Developments in Survey Sampling (N. L.
Johnsons and H. Smith Jr; Eds.). Wiley, New York, 506-527 (1965).
7. D.N.P. Murthy; M. Xie and R. Jiang; Weibull Models. John Wiley & Sons, New York (2004). Eugenics, 6,
13-25 (1934).
8. G.J. McLachlan and D. Peel; Finite Mixture Models. John Wiley & Sons (2000).
9. Ghosh; G.G. Hamedani; N. Bansal and M. Maadooliat; On the Mixtures of Weibull and Pareto (IV)
Distribution: An Alternative to Pareto Distribution. Communications in Statistics-Theory and Methods,
47(9), 2073-2084 (2018).
10. J.H. Kao; A Graphical Estimation of Mixed Weibull Parameters in Life-testing of Electron Tubes.
Technometrics, 1(4), 389-407 (1959).
11. K. Pearson; Contributions to the Mathematical Theory of Evolution. Philosophical Transactions of the Royal Society of London. A, 185, 71–110 (1894).
12. M.E. Ghitany; B. Atieh and S. Nadarajah; Lindley Distribution and Its Application. Mathematics and
Computers in Simulation, 78(4), 493-506 (2008).
13. N.L. Johnson; S. Kotz and N. Balakrishnan; Continuous Univariate Distributions, Vol. 1, John Wiley and
Sons (1994).
14. N.W. Andure; N.R. Bhandale and R.B. Ade; Exp-gamma Distribution as a New Life Time Model and Its
Application. Gradiva Review journal, 11(8), 39-48 (2025).
15. R.A. Fisher; The Effects of Methods of Ascertainment Upon the Estimation of Frequencies. Annals of
Eugenics, 6(1), 13-25 (1934).
16. R.A. Ganaie; C. Subramanian; V.P. Soumya; R. Shenbagaraja; M. Alam; D.V. Saraja; R. Kinjawadekar;
A.A. Rather and S.A. Dar; Enhancing Engineering Sciences with Uma Distribution: A Perfect Fit and
Valuable Contributions. Reliability: Theory & Applications, 18(4), 99-111 (2023).
17. R. Shanker (2015); Akash Distribution and Its Applications. International Journal of Probability and
Statistics, 4(3), 65-75 (2015).
18. R. Shanker and K.K. Shukla; Ishita Distribution and Its Applications. Biometrics & Biostatistics
International Journal, 5(2), 1-9 (2017)
19. R. Shanker; M. Ray and H.R. Prodhani; Weighted Komal Distribution with Properties and Applications.
International Journal of Statistics and Reliability Engineering, 10(3), 541-551 (2023).
20. S.F. Ateya; Maximum Likelihood Estimation under a Finite Mixture of Generalized Exponential
Distributions based on Censored Data. Statistical Papers, 55(2), 311-325 (2014).
21. S. Newcomb; A Generalized Theory of the Combination of Observations so as to Obtain the Best Result.
American Journal of Mathematics, 8(4), 343-366 (1886).
22. S. Sen; S. Maiti and N. Chandra; The Xgamma Distribution: Statistical Properties and Application. Journal
of Modern Applied Statistical Methods, 15(1), 774-788 (2016).
23. S. Stollmack and C.M. Harris; Failure-rate Analysis Applied to Recidivism Data. Operations Research,
22(6), 1139-1282 (1974).
24. V. Rajagopalan; R.A. Ganaie and A.A. Rather; A New Length Biased distribution with Applications.
Science, Technology and Development, 8(8), 161-174 (2019).
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