Powered Hazard Distribution through Order Statistics and Its Applications

Authors

  • M. I. Khan, Abdelfattah Mustafa,

Keywords:

Power hazard distribution, order statistics, moments, entropy, recurrence relations.

Abstract

This article addresses the distribution of order statistics of the power hazard distribution with graphical and quantitative measures along with cumulative residual entropy. We study the single and double moments and establish the recurrence relation between them. Finally, real data is analyzed to show the usefulness of our results.

Downloads

Download data is not yet available.

References

A. R. Mugdadi, “The least squares type estimation of the parameters in the power hazard function”, Applied Mathematics Computation, vol. 169, pp. 737–748, 2005.

A. R. Mugdadi, and A. Min, “Bayes estimation of the power hazard function,” Journal of Interdisciplinary Mathematics, vol. 12, no. 5, pp. 675-689, 2009.

K. Ismail, “Estimation of P(X

M. I. Khan, “The distribution having power hazard function (DPHF) based on ordered random variables”, Journal of Statistics Applications and Probability Letters, vol. 4, no. 1, pp. 31-36, 2017.

M.I. Khan, M. I. and M.A.R. Khan, “Generalized record values from distributions having power hazard function and characterization”, Journal of Statistics Applications and Probability, vol. 8, no. 2, pp. 103-111, 2019.

A. Mustafa and M. I. Khan, “The length-biased power hazard rate distribution with Applications”, Statistics in Transition New Series, vol. 23, no. 2, pp.1-16, 2022.

M. I. Khan and A. Mustafa, “Some properties of the weighted power hazard rate distribution with application”, Pakistan Journal of Statistics, vol. 38, no. 2, pp. 219-234, 2022.

M. I. Khan and A. Mustafa, “The transmuted power hazard rate distribution and its applications”, International Journal of Mathematics and Computer Science, vol. 17, no. 4, pp. 1697-1713, 2022.

A. Mustafa and M.I. Khan, “A new extension of power hazard distribution with applications”, Journal of Statistics Applications and Probability, vol. 12, no 3, pp. 1255-1267, 2023.

M.I. Khan, “Doubly truncated power-hazard rate distribution via generalized order statistics”, WSEAS Transactions on Mathematics, vol. 21, pp. 338-342, 2022.

M.I. Khan, “Moments of ordered random variates for transmuted power hazard distribution”, Journal of Applied Mathematics and Informatics, vol. 41, no. 5, pp. 1047-1056, 2023.

H.M. Aljohani, “Statistical inference of power hazard rate distribution in the presence of competing risks model with application”, Journal of Statistics Applications and Probability, vol. 12, S1, pp.1407-1418, 2023.

H.A. David and H.N. Nagaraja, “Order Statistics”, Third edition, John Wiley, New York, 2003.

B.C. Arnold, N. Balakrishnan and H.N. Nagaraja, “A First Course in Order Statistics”, John Wiley, New York, 1992.

P.C. Joshi, “Recurrence relations between moments of order statistics from exponential and truncated exponential distributions”, Sankhya, Series B, vol. 39, pp. 362-371, 1978.

U. Kamps, “Recurrence Relations for Moments of Order Statistics and Record Values”, In: Gritzmann, P., Hettich, R., Horst, R., Sachs, E. (eds) Operations Research, 91: Physica-Verlag HD, 1992.

Lee, In-Suk and Kim, Sang-Moon, “Recurrence relation and characterization of the Rayleigh distribution using order statistics”, Journal of Statistical Data and Information Science Society, vol. 10, no. 2, pp. 299-311, 1999.

N. Balakrishnan and H. J. Malik, “Order statistics from linear exponential distribution”, Part I: Increasing hazard rate case. Communication in Statistics– Theory and Methods, vol. 15, pp. 179-203, 1986.

M. Rao, Y. Chen and B.C. Yemuri, “Cumulative residual entropy: A new measure of information”, IEEE Transactions on Mathematics on Information Theory, vol. 50, no. 6, pp. 1220-1228, 2004.

A. Di, Crescenzo and M. Longobardi, “On cumulative entropies”, Journal of Statistical and Planning Inference, vol. 139, pp. 4072-4087, 2009.

P. Feigl and M. Zelen, “Estimation of exponential survival probabilities with concomitant information”, Biometrics, vol. 21, no. 4, pp. 826-838, 1965.

Downloads

Published

20.06.2024

How to Cite

M. I. Khan. (2024). Powered Hazard Distribution through Order Statistics and Its Applications. International Journal of Intelligent Systems and Applications in Engineering, 12(4), 600–608. Retrieved from https://ijisae.org/index.php/IJISAE/article/view/6264

Issue

Section

Research Article