A New Generalization of One Parameter Quasi Exponential Distribution: Properties and Applications

Anwar Hassan¹ , Nazima Akhter² , Bilal Ahmad Para³

Section:Research Paper, Product Type: Isroset-Journal
Vol.6 , Issue.2 , pp.339-354, Apr-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i2.339354

Online published on Apr 30, 2019

Copyright © Anwar Hassan, Nazima Akhter, Bilal Ahmad Para . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this article, we have introduced a new generalization of one parameter quasi exponential distribution using weighting technique. Important mathematical and statistical properties of the distribution have been derived and discussed. The expression for stochastic ordering, reliability measures and order statistics has been obtained. Maximum likelihood method of estimation along with Monte Carlo simulation has been discussed. Finally, real data set is analyzed to investigate the suitability of the proposed distribution in modeling lifetime data.

Key-Words / Index Term :
Quasi Exponential Distribution, Moments, Stochastic Ordering, Order Statistics, MLE, Lifetime Data

References :
[1]. Ajami, M., & Jahanshahi, S. M. (2017). Parameter Estimation in Weighted Rayleigh Distribution. Journal of Modern Applied Statistical Methods, 16(2), 256-276. doi:10.22237/jmasm/1509495240
[2]. Dennis, B. and Patil, G. (1984). The gamma distribution and weighted multimodal gamma distributions as models of population abtidance. Math. Biosciences, 68,187-212.
[3]. Fisher, R.A. (1934). The effects of methods of ascertainment upon the estimation of frequencies. Ann. Eugenics, 6, 13-25.
[4]. Ghitany, M., Alqallaf, F., Al-Mutairi, D., & Husain, H. (2011). A two-parameter weighted Lindley distribution and its applications to survival data. Mathematics and Computers in Simulation, 81(6), 1190-1201. doi:10.1016/j.matcom.2010.11.005
[5]. Gove, H. J (2003).Estimation and application of size-biased distributions in forestry, In Modeling Forest systems, A.Amaro,D. Reed and P.Soares CAB International Wallingford UK,201-212
[6]. Gross, A.J., & Clark, V. A. (1975). Survival Distributions: Reliability Applications in the Biometrical Sciences. John Wiley, New York, USA.
[7]. Hassan, A., Dar, S. A., & Para, B. A. (2018), On three Parameter Weighted Quasi Akash Distribution: Properties and Applications, IOSR Journal of Engineering (IOSRJEN), 08(11), 01-10.
[8]. Hassan, A., Wani, S.A., & Para, B. A. (2018). On three Parameter Weighted Quasi Lindley Distribution: Properties and Applications, International Journal of Scientific Research in Mathematical and Statistical Sciences, 5(5), pp. 210-224 DOI: https://doi.org/10.26438/ijsrmss/v5i5.210224.
[9]. Jing (2010). Weighted Inverse Weibull and Beta-Inverse Weibull Distribution, Georgia Southern University Digital Commons@Georgia Southern.
[10]. Para, B.A., & Jan, T. R. (2018). On three Parameter Weighted Pareto Type II Distribution: Properties and Applications in Medical Sciences. Applied Mathematics and Information Sciences Letters, 6 (1), 13-26.
[11]. Patil, G. P., & Rao, C. R. (1978). Weighted Distributions and Size-Biased Sampling with Applications to Wildlife Populations and Human Families. Biometrics, 34(2), 179. doi:10.2307/2530008
[12]. Shaked, M., & Shanthikumar, J. G. (1994). Stochastic Orders and their Applications. New York: Academic Press.
[13]. Taillie, C., Patil, G.P. and Hennemuth, R. (1995). Modelling and analysis of recruitment distributions. Ecological and Environmental Statistics, 2(4), 315-329.
[14]. Van Deusen, P.C. (1986). Fitting assumed distributions to horizontal point sample diameters. Forest Science, 32, 146-148.
[15]. Warren, W. (1975). Statistical distributions in forestry and forest products research. In: Patil, G.P., Kotz, S. and Ord, J.K. (eds) Statistical Distributions in Scientific Work, Vol. 2. D. Reidel, Dordrecht, The Netherlands, pp. 369-384.