Amal S. Hassan https://orcid.org/0000-0003-4442-8458 , Salwa M. Assar https:// orcid.org/0000-0001-7450-7486 , Ahmed M. Abdelghaffar https://orcid.org/0000-0002- 7163-927X
ARTICLE

(English) PDF

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.

KEYWORDS

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

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.

Back to top
Copyright © 2019 Statistics Poland