OJS  Vol.4 No.8 , September 2014
Hazard Rate Function Estimation Using Weibull Kernel
In this paper, we define the Weibull kernel and use it to nonparametric estimation of the probability density function (pdf) and the hazard rate function for independent and identically distributed (iid) data. The bias, variance and the optimal bandwidth of the proposed estimator are investigated. Moreover, the asymptotic normality of the proposed estimator is investigated. The performance of the proposed estimator is tested using simulation study and real data.

Cite this paper
Salha, R. , El Shekh Ahmed, H. and Alhoubi, I. (2014) Hazard Rate Function Estimation Using Weibull Kernel. Open Journal of Statistics, 4, 650-661. doi: 10.4236/ojs.2014.48061.
[1]   Salha, R. (2012) Hazard Rate Function Estimation Using Inverse Gaussian Kernel. The Islamic University of Gaza Journal of Natural and Engineering Studies, 20, 73-84.

[2]   Salha, R. (2013) Estimating the Density and Hazard Rate Functions Using the Reciprocal Inverse Gaussian Kernel. 15th Applied Stochastic Models and Data Analysis International Conference, Mataro (Barcelona), 25-28 June 2013.

[3]   Scaillet, O. (2004) Density Estimation Using Inverse and Reciprocal Inverse Gaussian Kernels. Nonparametric Statistics, 16, 217-226.

[4]   Watson, G. and Leadbetter, M. (1964) Hazard Analysis I. Biometrika, 51, 175-184.

[5]   Rice, J. and Rosenblatt, M. (1976) Estimation of the Log Survivor Function and Hazard Function. Sankhya Series A, 38, 60-78.

[6]   Cline, D.B.H. and Hart, J.D. (1991) Kernel Estimation of Densities of Discontinuous Derivatives. Statistics, 22, 69-84.

[7]   Schuster, E.F. (1985) Incorporating Support Constraints into Nonparametric Estimators of Densities. Communications in Statistics, Part A—Theory and Methods, 14, 1123-1136.

[8]   Silverman, B.W. (1986) Density Estimation for Statistics and Data Analysis. Chapman and Hall, London.

[9]   Cheng, M.Y., Fan, J. and Marron, J.S. (1997) On Automatic Boundary Corrections. The Annals of Statistics, 25, 1691-1708.

[10]   Zhang, S. and Karunamuni, R.J. (1998) On Kernel Density Estimation near Endpoints. Journal of Statistical Planning and Inference, 70, 301-316.

[11]   Chen, S.X. (2000) Probability Density Function Estimation Using Gamma Kernels. Annals of the Institute of Statistical Mathematics, 52, 471-480.