Special Issue 2022 – Call for Papers
A New Role for Statistics: The Joint Special Issue of "Statistics in Transition New Series" (SiTns) and "Statystyka Ukraïny" (SU)
Abdelfattah Mustafa https://orcid.org/0000-0002-8551-6115 , M. I. Khan https://orcid.org/0000-0002-5793-9786

© Abdelfattah Mustafa, M. I. Khan. Article available under the CC BY-SA 4.0 licence

ARTICLE

(English) PDF

ABSTRACT

In this article, the length-biased power hazard rate distribution has introduced and investigated several statistical properties. This distribution reports an extension of several probability distributions, namely: exponential, Rayleigh, Weibull, and linear hazard rate. The procedure of maximum likelihood estimation is taken for parameters. Finally, the applicability of the model is explored by three real data sets. To examine, the performance of the technique, a simulation study is extracted.

KEYWORDS

length-biased, power hazard rate distribution, maximum likelihood estimation

REFERENCES

Ajami, M., Jahanshahi S. M. A., (2017). Parameter estimation in weighted Rayleigh distribution. Journal of Modern Applied Statistical Methods, 16(2), pp. 256–276.

Al-Khadim, A. K., Hussein A. N., (2014). New proposed length-biased weighted Exponential and Rayleigh distribution with application. Mathematical Theory and Modeling, 4, pp. 2224–5804.

Balakrishnan, N., Victor, L., Antonio, S., (2010). A mixture model based on Birnhaum- Saunders Distributions, A study conducted by Authors regarding the Scores of the GRASP (General Rating of Affective Symptoms for Preschoolers), in a city located at South Part of the Chile.

Birnbaum, Z. W., Saunders, S. C., (1969). Estimation for a family of life distribution with applications to fatigue. Journal of Applied Probability, 6(2), pp. 328–347.

Cox, D. R., (1962). Renewal Theory. New York, NY: Barnes & Noble.

Das, K. K., Roy, T. D., (2011). Applicability of length-biased generalized Rayleigh distribution. Advances in Applied Science Research, 2, pp. 320–327.

Das, K. K., Roy, T. D., (2011). On some length-biased weighted Weibull distribution. Advances in Applied Science Research, 2, pp. 465–475.

Gupta, P. L., Tripathi, R. C., (1990). Effect of length-biased sampling on the modeling error. Communications Statistics - Theory and Methods, 19, pp. 1483–1491.

Gupta, R. C., Keating, J. P., (1985). Relations for reliability measures under length-biased sampling. Scandanavian Journal of Statistics, 13, pp. 49–56.

Ismail, K., (2014). Estimation of for distribution having power hazard function. Pakistan Journal of Statistics, 30, pp. 57–70.

Lawless, J. F., (2003). Statistical Models and Methods for Lifetime Data, 2nd Edition, Weiley, Canada.

Mir, K. A., Ahmed, A., Reshi, J. A., (2013). On Size-biased Exponential Distribution. Journal of Modern Mathematics and Statistics, 7(2), pp. 21–25.

Khattree, R., (1989). Characterization of inverse-Gaussian and gamma distributions through their length-biased distributions. IEEE Transactions on Reliability, 38, pp. 610–611.

Mahmoud, M. R., Mandouh, R. M., (2013). On the Transmuted Fréchet Distribution. Journal of Applied Sciences Research, 9(10), pp. 5553–5561.

Modi, K., (2015). Length-biased Weighted Maxwell distribution. Pakistan Journal of Statistics and Operation Research, 11(4), pp. 465–472.

Mudasir, S., Ahmad, S. P., (2018). Characterization and estimation of the length-biased Nakagami distribution. Pakistan Journal of Statistics and Operation Research, 14(3), pp. 697–715.

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

Mugdadi, A. R., Min, A., (2009). Bayes estimation of the power hazard function. Journal of Interdisciplinary Mathematics, 12, pp. 675–689.

Nanuwong, N., Bodhisuwan,W., (2014). Length-biased nu Pareto distribution and its structural properties with application. Journal of Mathematics and Statistics, 10, pp. 49–57.

Oluyede, B. O., (1999). On inequalities and selection of experiments for length-biased distributions. Probability in the Engineering and Informational Sciences, 13, pp. 169–185.

Praveen, Z., Ahmad, M., (2018). Some properties of size- biased weighted Weibull distribution. International Journal of Advanced and Applied Sciences, 5(5), pp. 92–98.

Ratnaparkhi, M. V., Naik-Nimbalkar, U. V., (2012). The length-biased lognormal distribution and its application in the analysis of data from oil field exploration studies. Journal of Modern Applied Statistical Methods, 11, pp. 225–260.

Saghir, A., Khadim, A., Lin, Z., (2017). The Maxwell length-biased distribution: Properties and Estimation. Journal of Statistical Theory and Practice, 11, pp. 26–40.

Saghir, A., Tazeem, S., Ahmad, I., (2016). The length-biased weighted exponentiated inverted Weibull distribution. Cogent Mathematics, 3(1), DOI: 10.1080/23311835.2016.1267299.

Seenoi, P., Supapa, K.T., Bodhisuwan, W., (2014). The length-biased exponentiated inverted Weibull Distribution. International Journal of Pure and Applied Mathematics, 92, pp. 191–206.

Shaban, S.A., Boudrissa, N. A., (2007). The Weibull length-biased distribution: Properties and estimation. Interstat, http://interstat.statjournals.net/YEAR/2007/articles/0701002.pdf

Tarvirdizade, B., Nematollahi, N., (2016). Parameter estimation based on record data from power hazard rate distribution. 13th Iranian Statistical Conference, Kerman, Iran.

Tarvirdizade, B., Nematollahi, N., (2020). Inference on P(X >Y) based on record values from power hazard rate distribution. Journal of Computational Statistics and Modelling, 1(1), pp. 59–76.

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