Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Kernel Inference on the Inverse Weibull Distribution

  • Maswadah, M. (Department of Mathematics, Faculty of Science, South Valley University)
  • Published : 2006.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, the Inverse Weibull distribution parameters have been estimated using a new estimation technique based on the non-parametric kernel density function that introduced as an alternative and reliable technique for estimation in life testing models. This technique will require bootstrapping from a set of sample observations for constructing the density functions of pivotal quantities and thus the confidence intervals for the distribution parameters. The performances of this technique have been studied comparing to the conditional inference on the basis of the mean lengths and the covering percentage of the confidence intervals, via Monte Carlo simulations. The simulation results indicated the robustness of the proposed method that yield reasonably accurate inferences even with fewer bootstrap replications and it is easy to be used than the conditional approach. Finally, a numerical example is given to illustrate the densities and the inferential methods developed in this paper.

Keywords

References

  1. Abramson, I. (1982). On Bandwidth Variation In Kernel Estimates: A Square Root Law. The Annals of Statistics, Vol. 10, 1217-1223 https://doi.org/10.1214/aos/1176345986
  2. Calabria, R. and Pulcini, G. (1990). On the maximum likelihood and least squares estimation In the inverse Weibull distribution. Statistica Applicata, Vol. 2, 53-66
  3. Calabria, R. and Pulcini, G. (1992). Bayes probability intervals In a load-strength model. Communications in Statistics-Theory & Method, Vol. 21, 1811-1824
  4. Dumonceaux, R. and Antle, C.E. (1973). Discrimination between the Log -normal and Weibull Distribution. Technometrics, Vol. 15, 923-926 https://doi.org/10.2307/1267401
  5. Guillamon, A. Navarro, J. and Ruiz, J.M. (1998). Kernel density estimation using weighted data. Communications in Statistics-Theory & Method, Vol. 27, 2123-2135 https://doi.org/10.1080/03610929808832217
  6. Guillamon, A. Navarro, J. and Ruiz, J.M. (1999). A note on kernel estimators for positive valued random variables. Sankhya: The Indian Journal of Statistics. Vol. 6, Ser. A, 276-281
  7. Johnson, N.L., Kotz, S. and Balakrishnan, N. (1995). Continuous Univariate Distributions-II. 2-nd edition. John Wiley & Sons
  8. Jones, M.C. (1991). Kernel density estimation for length biased data. Biometerika, Vol. 78, 511-519 https://doi.org/10.1093/biomet/78.3.511
  9. Kulczycki, P. (1999). Parameter, Identification Using Bayes and Kernel Approaches. Proceedings of the National Science Council ROC(A), Vol. 23, 205-213
  10. Lawless, J.F. (1982). Statistical Models & Methods for Lifetime Data, John Wiley & Sons. New York
  11. Maswadah, M. (2003). Conditional confidence interval estimation for the Inverse Weibull distribution based on censored generalized order statistics. Journal of Statistical Computation & Simulations, Vol. 73, 87-898
  12. Scott D.W. (1992). Multivariate Density Estimation. Wiley-interscience. New York
  13. Terrell, G.R. (1990). The maximal smoothing principle in density estimation. Journal of the American Statistical Association, Vol. 85, 470-477 https://doi.org/10.2307/2289786