Transmuted Inverse Xgamma Distribution: Statistical Properties, Classical Estimation Methods and Data Modeling
DOI:
https://doi.org/10.6092/issn.1973-2201/15277Keywords:
Transmuted inverse Xgamma distribution, Lifetime distribution, Hazard rate function, Classical estimation, SimulationAbstract
In this article, a new variant of Inverse Xgamma distribution is introduced by using the quadratic rank transmutation map (QRTM), named as Transmuted Inverse Xgamma (TIXG) distribution. The proposed model is positively skewed and has flexibility in the hazard rate function. A comprehensive account of mathematical and statistical properties of the newly obtained lifetime model are provided. Explicit expressions for moments, moment generating function, quantile functions, stochastic orderings, ageing intensity function and order statistics are formulated. We briefly discuss different classical estimations, including the maximum likelihood, maximum product spacings, least square, weighted least square and Cram`er-Von-Mises estimation methods. Monte Carlo simulation is carried out to compare the performance of the different estimation methods. Finally, to demonstrate the applicability of the model in real life, an illustrative example is performed by analyzing an environmental science dataset.
References
M. V. AARSET (1987). How to identify a bathtub hazard rate. IEEE Transactions on Reliability, 36, no. 1, pp. 106–108.
A. AHMAD, S. AHMAD, A. AHMED (2014). Transmuted inverse Rayleigh distribution: a generalization of the inverse Rayleigh distribution. Mathematical Theory and Modeling, 4, no. 7, pp. 90–98.
A. A. AL-BABTAIN, I. ELBATAL, H. M. YOUSOF (2020). A new three parameter Fréchet model with mathematical properties and applications. Journal of Taibah University for Science, 14, no. 1, pp. 265–278.
G. R. ARYAL, C. P. TSOKOS (2009). On the transmuted extreme value distribution with application. Nonlinear Analysis: Theory, Methods & Applications, 71, no. 12, pp. e1401–e1407.
P. BANERJEE, S. BHUNIA (2022). Exponential transformed inverse Rayleigh distribution: statistical properties and different methods of estimation. Austrian Journal of Statistics, 51, no. 4, pp. 60–75.
A. M. BASHEER (2019). Alpha power inverse Weibull distribution with reliability application. Journal of Taibah University for Science, 13, no. 1, pp. 423–432.
D. K. BHAUMIK, R. D. GIBBONS (2006). One-sided approximate prediction intervals for at least p of m observations from a gamma population at each of r locations. Technometrics, 48, no. 1, pp. 112–119.
D. K. BHAUMIK, K. KAPUR, R. D. GIBBONS (2009). Testing parameters of a gamma distribution for small samples. Technometrics, 51, no. 3, pp. 326–334.
S. BHUNIA, P. BANERJEE (2022). Some properties and different estimation methods for inverse A( ) distribution with an application to tongue cancer data. Reliability: Theory & Applications, 17, no. 1 (67), pp. 251–266.
H. D. BIÇER (2019). Properties and inference for a new class of XGamma distributions with an application. Mathematical Sciences, 13, no. 4, pp. 335–346.
A. BOWLEY (1920). Elements of Statistics. v. 8. P. S. King & Son, Limited.
G. CASELLA, R. L. BERGER (2002). Statistical Inference. Duxbury Press, Pacific Grove, 2nd ed.
R. C. H. CHENG, N. A. K. AMIN (1979). Maximum product of spacings estimation with applications to the lognormal distribution. Tech. rep., Department of Mathematics, University of Wales.
R. C. H. CHENG, N. A. K. AMIN (1983). Maximum product of spacings estimation with applications to the lognormal distribution. Journal of the Royal Statistical Society-Series B, 45, no. 3, pp. 394–403.
C. CHESNEAU, L. TOMY, J. GILLARIOSE (2021). A new modified Lindley distribution with properties and applications. Journal of Statistics and Management Systems, 24, no. 7, pp. 1383–1403.
R. B. D’AGOSTINO, M. A. STEPHENS (1986). Goodness-of-Fit Techniques. Marcel Dekker, New York.
J. T. EGHWERIDO, J. O.OGBO, A. E.OMOTOYE (2021). The Marshall-Olkin Gompertz distribution: properties and applications. Statistica, 81, no. 2, pp. 183–215.
R. JIANG, P. JI, X. XIAO (2003). Aging property of unimodal failure rate models. Reliability Engineering & System Safety, 79, no. 1, pp. 113–116.
M. S. KHAN, R. KING, I. L. HUDSON (2017). Transmuted generalized exponential distribution: a generalization of the exponential distribution with applications to survival data. Communications in Statistics-Simulation andComputation, 46, no. 6, pp. 4377–4398.
K. KRISHNAMOORTHY, T. MATHEW, S. MUKHERJEE (2008). Normal-based methods for a gamma distribution: prediction and tolerance intervals and stress-strength reliability. Technometrics, 50, no. 1, pp. 69–78.
A. LUCEÑO (2006). Fitting the generalized Pareto distribution to data using maximum goodness-of-fit estimators. Computational Statistics & Data Analysis, 51, no. 2, pp. 904–917.
P. MACDONALD (1971). Comments and queries comment on “an estimation procedure for mixtures of distributions” by Choi and Bulgren. Journal of the Royal Statistical Society-Series B, 33, no. 2, pp. 326–329.
F. MEROVCI (2013). Transmuted Rayleigh distribution. Austrian Journal of Statistics, 42, no. 1, pp. 21–31.
J. MOORS (1988). A quantile alternative for kurtosis. Journal of the Royal Statistical Society-Series D, 37, no. 1, pp. 25–32.
A. K.NANDA, S. BHATTACHARJEE, S. ALAM (2007). Properties of aging intensity function. Statistics & Probability Letters, 77, no. 4, pp. 365–373.
M.NASSAR, S.DEY, D.KUMAR (2018). Anewgeneralization of the exponentiated Pareto distribution with an application. American Journal of Mathematical and Management Sciences, 37, no. 3, pp. 217–242.
R CORE TEAM (2021). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
B. RANNEBY (1984). The maximum spacing method. an estimation method related to the maximum likelihood method. Scandinavian Journal of Statistics, 11, no. 2, pp. 93–112.
G. S. RAO, S. MBWAMBO, et al. (2019). Exponentiated inverse Rayleigh distribution and an application to coating weights of iron sheets data. Journal of Probability and Statistics, 2019, no. 1, p. 7519429.
B. SEAL, P. BANERJEE, S. BHUNIA, S. K. GHOSH (2023). Bayesian estimation in Rayleigh distribution under a distance type loss function. Pakistan Journal of Statistics and Operation Research, 19, no. 2, pp. 219–232.
S. SEN,N. CHANDRA, S. S.MAITI (2017). The weighted xgamma distribution: properties and application. Journal of Reliability and Statistical Studies, pp. 43–58.
S. SEN, N. CHANDRA, S. S. MAITI (2018). Survival estimation in xgamma distribution under progressively type-ii right censored scheme. Model Assisted Statistics and Applications, 13, no. 2, pp. 107–121.
S. SEN, S. S.MAITI,N.CHANDRA (2016). The xgamma distribution: statistical properties and application. Journal of Modern Applied Statistical Methods, 15, no. 1, p. 38.
M. SHAKED, J. SHANTHIKUMAR (1994). Stochastic Orders and their Applications. Academic Press, Boston.
W. T. SHAW, I. R. C. BUCKLEY (2009). The alchemy of probability distributions: beyond gram-charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map. arXiv preprint arXiv:0901.0434.
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.
A. S. YADAV, M. SAHA, H. TRIPATHI, S. KUMAR (2021). The exponentiated xgamma distribution: a new monotone failure rate model and its applications to lifetime data. Statistica, 81, no. 3, pp. 303–334.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Statistica
This work is licensed under a Creative Commons Attribution 3.0 Unported License.
