# The Exponentiated XGamma Distribution: a New Monotone Failure Rate Model and Its Applications to Lifetime Data

## DOI:

https://doi.org/10.6092/issn.1973-2201/10578## Keywords:

Xgamma distribution, Moments, Generating function, Conditional moments, Reliability curve, Different methods of estimation## Abstract

In this article, the exponentiated version of xgamma distribution (XGD) has been introduced, named as exponentiated xgamma distribution (EXGD). The proposed model is positively skewed and possess some interesting shapes of hazard rate, i.e., increasing, decreasing and bathtub. Different distributional properties of proposed model, viz., moments, generating functions, mean deviation, quantile function, order statistics, reliability curves and indices etc. have been derived. The estimation of the parameters, survival function and hazard function of EXGD have been approached

by different methods of estimation. A Simulation study is carried out to compare the performances of the different estimators obtained via different methods of estimation. Two real data sets have been analyzed to illustrate the applicability of the proposed model.

## References

A. Z. AFIFY, O. A. MOHAMED (2020). A new three-parameter exponential distribution with variable shapes for the hazard rate: Estimation and applications. Mathematics, 8, no. 1, pp. 1–17.

A. Z. AFIFY, M.NASSAR, G. M. CORDEIRO, D. KUMAR (2020). The weibull marshall–olkin lindley distribution: properties and estimation. Journal of Taibah University for Science, 14, no. 1, pp. 192–204.

A. Z. AFIFY, Z. M. NOFAL, A. E. H. N. EBRAHEIM (2015). Exponentiated transmuted generalized rayleigh distribution: A new four parameter rayleigh distribution. Pakistan Journal of Statistics and Operation Research, 11, no. 1, pp. 115–134.

A. Z. AFIFY, H. M. YOUSOF, G. HAMEDANI, G. R. ARYAL (2016). The exponentiated weibull-pareto distribution with application. Journal of Statistical Theory and Applications, 15, no. 4, pp. 326–344.

W. BARRETO-SOUZA, F. CRIBARI-NETO (2009). A generalization of the exponentialpoisson distribution. Statistics & Probability Letters, 79, no. 24, pp. 2493–2500.

A. L. BOWLEY (1920). Element of Statistics. P S King and Son, Ltd, New York.

K. P. BURNHAM, D. R. ANDERSON (2002). Model selection and multimodal inference: A practical information-theoretic approach. Second ed. New York, Springer.

R. CHENG, N. AMIN (1983). Estimating parameters in continuous univariate distributions with a shifted origin. Journal of the Royal Statistical Society: Series B (Methodological), 45, no. 3, pp. 394–403.

G. M. CORDEIRO, A. Z. AFIFY, H. M. YOUSOF, R. R. PESCIM, G. R. ARYAL (2017). The exponentiated weibull-h family of distributions: Theory and applications. Mediterranean Journal of Mathematics, 14, no. 4, pp. 1–22.

R. D. GUPTA, D. KUNDU (2001). Exponentiated exponential family: an alternative to gamma and weibull distributions. Biometrical Journal: Journal of Mathematical Methods in Biosciences, 43, no. 1, pp. 117–130.

C. R. C. H, A.N. A. K (1979). Maximum product-of-spacings estimation with applications to the log-normal distribution. University ofWales IST, Math Report, pp. 79–1.

D. HINKLEY (1977). On quick choice of power transformation. Journal of the Royal Statistical Society: Series C (Applied Statistics), 26, no. 1, pp. 67–69.

R. IHAKA, R. GENTLEMAN (1996). R: a language for data analysis and graphics. Journal of computational and graphical statistics, 5, no. 3, pp. 299–314.

D. V. LINDLEY (1958). Fiducial distributions and bayes’ theorem. Journal of the Royal Statistical Society. Series B (Methodological), pp. 102–107.

J. MOORS (1988). A quantile alternative for kurtosis. Journal of the Royal Statistical Society: Series D (The Statistician), 37, no. 1, pp. 25–32.

G. S.MUDHOLKAR, D. K. SRIVASTAVA (1993). Exponentiated weibull family for analyzing bathtub failure-rate data. IEEE transactions on reliability, 42, no. 2, pp. 299–302.

S. NADARAJAH, H. S. BAKOUCH, R. TAHMASBI (2011). A generalized lindley distribution. Sankhya B, 73, no. 2, pp. 331–359.

M.NASSAR, A. Z. AFIFY, M. SHAKHATREH (2020). Estimation methods of alpha power exponential distribution with applications to engineering and medical data. Pakistan Journal of Statistics and Operation Research, pp. 149–166.

B. RANNEBY (1984). The maximum spacing method. an estimation method related to the maximum likelihood method. Scandinavian Journal of Statistics, pp. 93–112.

S. SEN, A. Z. AFIFY, H. AL-MOFLEH, M. AHSANULLAH (2019). The quasi xgammageometric distribution with application in medicine. Filomat, 33, no. 16, pp. 5291–5330.

S. SEN, S. S.MAITI,N.CHANDRA (2016). The xgamma distribution: statistical properties and application. Journal of Modern Applied Statistical Methods, 15, no. 1, pp. 774–788.

R. SHANKAR (2015). Akash distribution and its application. International Journal of Probability and Statistics, 4, no. 3, pp. 65–75.

A. I. SHAWKY, R. A. BAKOBAN (2006). Certain characteristics of the exponentiated gamma distributions. Journal of Statistical Science, 3, no. 2, pp. 151–164.

J. SURLES, W. PADGETT (2001). Inference for reliability and stress-strength for a scaled burr type x distribution. Lifetime data analysis, 7, no. 2, pp. 187–200.

J. J. SWAIN, S. VENKATRAMAN, J. R. WILSON (1988). Least-squares estimation of distribution functions in johnson’s translation system. Journal of Statistical Computation and Simulation, 29, no. 4, pp. 271–297.

A. S. YADAV, S. S.MAITI, M. SAHA (2019). The inverse xgamma distribution: statistical properties and different methods of estimation. Annals of Data Science, pp. 1–19.

## Downloads

## Published

## How to Cite

*Statistica*,

*81*(3), 303–334. https://doi.org/10.6092/issn.1973-2201/10578

## Issue

## Section

## License

Copyright (c) 2021 Statistica

This work is licensed under a Creative Commons Attribution 3.0 Unported License.