Statistical Properties and Estimation of Power-Transmuted Inverse Rayleigh Distribution

Publications

Share / Export Citation / Email / Print / Text size:

Statistics in Transition New Series

Polish Statistical Association

Central Statistical Office of Poland

Subject: Economics, Statistics & Probability

GET ALERTS

ISSN: 1234-7655
eISSN: 2450-0291

DESCRIPTION

33
Reader(s)
88
Visit(s)
0
Comment(s)
0
Share(s)

SEARCH WITHIN CONTENT

FIND ARTICLE

Volume / Issue / page

Related articles

VOLUME 21 , ISSUE 3 (September 2020) > List of articles

Statistical Properties and Estimation of Power-Transmuted Inverse Rayleigh Distribution

Amal S. Hassan / Salwa M. Assar / Ahmed M. Abdelghaffar

Keywords : transmuted inverse Rayleigh, mean residual life function, maximum likelihood, percentiles

Citation Information : Statistics in Transition New Series. Volume 21, Issue 3, Pages 93-107, DOI: https://doi.org/10.21307/stattrans-2020-046

License : (CC BY-NC-ND 4.0)

Received Date : 21-November-2019 / Accepted: 14-June-2020 / Published Online: 20-September-2020

ARTICLE

ABSTRACT

A three-parameter continuous distribution is constructed, using a power transformation related to the transmuted inverse Rayleigh (TIR) distribution. A comprehensive account of the statistical properties is provided, including the following: the quantile function, moments, incomplete moments, mean residual life function and Rényi entropy. Three classical procedures for estimating population parameters are analysed. A simulation study is provided to compare the performance of different estimates. Finally, a real data application is used to illustrate the usefulness of the recommended distribution in modelling real data.

Content not available PDF Share

FIGURES & TABLES

REFERENCES

AHMAD, A., AHMAD, S.P., AHMED, A., (2014). Transmuted inverse Rayleigh distribution: A generalization of the inverse Rayleigh distribution. Mathematical Theory and Modeling, 4(7), pp. 90−98.

BJERKEDAL, T., (1960). Acquisition of resistance in guinea pigs infected with different doses of virulent tubercle bacilli. American Journal of Epidemiology, 72(1), pp. 130−148.

BOX, G. E. P., COX, D. R., (1964). An analysis of transformations. Journal of the Royal Statistical Society, Series B, 26, pp. 211−252.

BUTLER, R.J., MCDONALD, J. B., (1989). Using of incomplete moments to measure inequality. Journal of Econometrics, 42(1), pp. 109−119.

DEY, S., (2012). Bayesian estimation of the parameter and reliability function of an inverse Rayleigh distribution. Malaysian Journal of Mathematical Sciences, 6(1), pp. 113−124.

ELGARHY, M., ALRAJHI, S., (2018). The odd Fréchet inverse Rayleigh distribution: Statistical properties and applications. Journal of Nonlinear Sciences and Applications, 12, pp. 291−299.

FAN, G., (2015). Bayes estimation for inverse Rayleigh model under different loss functions. Research Journal of Applied Sciences, Engineering and Technology, 9(12), pp. 1115−1118.

FATIMA, K., AHMAD, S. P., (2017). Weighted inverse Rayleigh distribution. International Journal of Statistics and Systems, 12(1), pp. 119−137.

GHARRAPH, M.K., (1993). Comparison of estimators of location measures of an inverse Rayleigh distribution. The Egyptian Statistical Journal, 37, pp. 295−309.

HAQ, M. A., (2015). Transmuted exponentiated inverse Rayleigh distribution. Journal of Statistics Applications and Probability, 5(2), pp. 337−343.

HAQ, M. A., (2016). Kumaraswamy exponentiated inverse Rayleigh distribution. Mathematical Theory and Modeling, 6(3), pp. 93−104.

KHAN, M. S., (2014). Modified inverse Rayleigh distribution. International Journal of Computer Applications, 87(13), pp. 28−33.

KHAN, M. S., KING, R., (2015). Transmuted modified inverse Rayleigh distribution. Austrian Journal of Statistics, 44, pp. 17−29.

LEAO, J., SAULO, H., BOURGUIGNON, M., CINTRA, J., REGO, L., CORDEIRO, G., (2013). On some properties of the beta Inverse Rayleigh distribution. Chilean Journal of Statistics, 4(2), pp. 111−131.

MOHSIN, M., SHAHBAZ, M. Q., (2005). Comparison of negative moment estimator with maximum likelihood estimator of inverse Rayleigh distribution. Pakistan Journal of Statistics Operation Research, 1, pp. 45−48.

PANWAR, M. S., SUDHIR, B. A., BUNDEL, R., TOMER, S. K., (2015). Parameter estimation of Inverse Rayleigh distribution under competing risk model for masked data. Journal of Institute of Science and Technology, 20(2), pp. 122−127.

RASHEED, H. A., ISMAIL, S. Z., JABIR, A. G., (2015). A comparison of the classical estimators with the Bayes estimators of one parameter inverse Rayleigh distribution. International Journal of Advanced Research, 3(8), pp. 738−749.

RASHEED, H. A., AREF, R. K. H., (2016). Reliability estimation in inverse Rayleigh distribution using precautionary loss function. Mathematics and Statistics Journal, 2(3), pp. 9−15.

SINDHU, T. N., ASLAM, M., FEROZE, N., (2013). Bayes estimation of the parameters of the inverse Rayleigh distribution for left censored data. ProbStat Forum, 6, pp. 42−59.

SOLIMAN, A., AMIN, E. A., ABD-EI AZIZ, A. A., (2010). Estimation and prediction from inverse Rayleigh distribution based on lower record values. Applied Mathematical Sciences, 4, pp. 3057−3066.

TRAYER, V. N., (1964). Proceedings of the Academy of Science Belarus, USSR.

VODA, V. G. H., (1972). On the inverse Rayleigh distributed random variable. Rep. Statistics Application and Research, JUSE., 19(4), pp. 13−21.

EXTRA FILES

COMMENTS