Order Statistics based on Exponential and Weibull Distributions

Viswanathan. N; Ramakrishnan. M

doi:https://doi.org/10.14445/22315373/IJMTT-V53P537

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 53 | Number 4 | Year 2018 | Article Id. IJMTT-V53P537 | DOI : https://doi.org/10.14445/22315373/IJMTT-V53P537

Order Statistics based on Exponential and Weibull Distributions

Viswanathan. N, Ramakrishnan. M

Citation :

Viswanathan. N, Ramakrishnan. M, "Order Statistics based on Exponential and Weibull Distributions," International Journal of Mathematics Trends and Technology (IJMTT), vol. 53, no. 4, pp. 293-300, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V53P537

Abstract

Order statistics are widely used in Statistical modeling and its Statistical inference, which describes the random variables that are arranged in order of magnitude, frequently with respect to time. Order statistics deals with the properties and applications of ordered random variables and their functions. This study particularly focuses on two different failure time structures with Exponential and Weibull distributions. In particular, the study uses one parameter Exponential and Three parameter Weibull distributions. Distributions of Ordered statistics based on samples from exponential distribution are derived. Also their Moments, Skewness and Kurtosis were considered. Data were simulated and using them the parameters and moments of the distributions are estimated. All the estimated parameters are found to be very close to the population parameter with which the simulation has been initiated. The parameters are estimated with better accuracy. On the whole the study uses effectively the concept of Order Statistics in the domain of Reliability with focus on estimation and testing of its crucial parameters.

Keywords

Order Statistics, Moments, Simulation, Parameter Estimation.

References

[1] W. Weibull, “A statistical distribution functions with wide applicability”, J. Appl. Mech. vol. 18, pp. 292-297, 1951.
[2] J. F. Lawless, Statistical Models and Methods for Lifetime Data. Wiley, New York, 1982.
[3] H. Rinne, The Weibull Distribution The Hand book. Chapman & Hall. New York, 2009.
[4] R. Jiang and D.N.P. Murthy, “Comment on a general linear–regression analysis applied to the three–parameter Weibull distribution”, IEEE Transactions on Reliability, vol. 46, pp. 389–393, 1997.
[5] V. Bartkute and L. Sakalauskas., “The method of three-parameter Weibull distribution estimation”, Acta ET Commentationes Universitatis Tartuensis De Mathematica, vol. 12, pp. 65-78, 2008.
[6] L.J. Bain and M.E. Engelhardt, M . Statistical Analysis of Reliability and Life Testing Models, 2nd Edition Marcel Dekker,INC . New York, 1991.
[7] L.J. Bain and C.E. Antle. “Estimation of parameters in the Weibull distribution”. Technometrics, vol. 9, 621-627, 1967.
[8] D.J. Davis.” An analysis of some failure data”. Journal of American Statistical. Association.vol. 47, pp. 113-150, 1952.
[9] Barry C. Arnold, N. Balakrishnan and H.N. Nagaraja, A First Course in Order Statistics, Wiley & Sons, Inc., 1992.
[10] H.A. David and H.N. Nagaraja, Order Statistics third edition,John Wiley & Sons, Inc., 2003.
[11] J. Lieblein, “On moments of order statistics from the Weibull distribution”,Ann. Math. Statist. vol. 26, pp. 330-333. 1955.