International Journal of Statistics and Reliability Engineering

No Publication Cost

Vol 11, No 1:

subscription

Arctan-Chen Distribution with Properties and Application

Abstract

In this study, we have introduced a three-parameter continuous probability distribution using arctan family of distribution and Chen distribution. Probability distribution function, probability density function as well as some statistical properties of the proposed model is included in this article. Parameters of the model are estimated using maximum likelihood estimation, least square method and Creamers – von Mises method of estimation. For testing the applicability of the model, a real data set is taken. For model comparison, five other models available in literature are taken. For comparison of the model, Akaike information criterion, Bayesian information criterion and Hannan-Quinn information criterion are used. For validity testing, Kolmogrov – Simonov test, Cramer’s – Von Mises test and Anderson-Darling test are used. Graphical methods like P-P plots and Q-Q plots are used for validity testing. To evaluate the accuracy of the estimation procedure, a simulation experiment is conducted, revealing a decrease in biases and mean square errors as sample sizes increase, even when working with small samples. The computations and graphical representations have been done by using R.

Full Text

PDF

References

1. A. El-Gohary; A. Alshamrani and A.N. Al-Otaibi; The Generalized Gompertz Distribution. Applied
Mathematical Modelling, 37(1-2), 13-24 (2013).
2. A.J. Lemonte; A New Exponential-Type Distribution with Constant, Decreasing, Increasing, Upside-Down
Bathtub and Bathtub-Shaped Failure Rate Function. Computational Statistics & Data Analysis, 62, 149-170
(2013).
3. A.K. Chaudhary; L.P. Sapkota and V. Kumar; Some Properties and Applications of Arctan Generalized
Exponential Distribution. International Journal of Innovative Research in Science, Engineering and
Technology (IJIRSET), 10(1), 456-468 (2021).
4. A.K. Srivastava and V. Kumar; Markov Chain Monte Carlo Methods for Bayesian Inference of the Chen
Model. International Journal of Computer Information Systems, 2(2), 7-14 (2011).
5. B. Tarvirdizade and M. Ahmadpour; A New Extension of Chen Distribution with Applications to Lifetime
Data. Communications in Mathematics and Statistics, 9, 23-28, (2021).
6. D. Bhati; M.A. Malik and H.J. Vaman; Lindley–Exponential distribution: Properties and Applications.
METRON, 73(3), 335–357 (2015).
7. E. Gómez-Déniz and E. Calderín-Ojeda; Modelling Insurance Data with the Pareto ArcTan
Distribution. ASTIN Bulletin: The Journal of the IAA, 45(3), 639-660 (2015).
8. E. Gómez Déniz; E. Calderín Ojeda and J.M. Sarabia; The Arctan Family of Distributions: New Results with
Applications. Chilean Journal of Statistics, 13(1), 113-132 (2022).
9. F.A. Bhatti; G.G. Hamedani; S.M. Najibi and M. Ahmad; On the Extended Chen Distribution: Development,
Properties, Characterizations and Applications. Annals of Data Science, 8(1), 159-180 (2021).
10. J. Moors; A Quantile Alternative for Kurtosis. The Statistician, 37, 25-32 (1988).
11. M.D. Nichols and W.J. Padgett; A Bootstrap Control Chart for Weibull Percentiles. Quality and Reliability
Engineering International, 22(2), 141-151 (2006).
12. M.M. Ristić and S. Nadarajah; A New Lifetime Distribution. Journal of Statistical Computation and
Simulation, 84(1), 135-150 (2014).
13. P.E. Oguntunde; A. Adejumo and O.S. Balogun; Statistical Properties of the Exponentiated Generalized
Inverted Exponential Distribution. Applied Mathematics, 4(2), 47-55 (2014).
14. R Core Team; R: A language and environment for statistical computing. R Foundation for Statistical
Computing, Vienna, Austria, (2018). URL: https://www.R-project.org/.
15. R.K. Joshi and V. Kumar; Lindley-Chen Distribution with Applications. International Journals of
Engineering, Science & Mathematics (IJESM), 9(10), 12-22 (2020)
16. Z. Chen; A New Two-Parameter Lifetime Distribution with Bathtub Shape or Increasing Failure Rate
Function. Statistics & Probability Letters, 49(2), 155-161 (2000).

ISSN(P) 2350-0174

ISSN(O) 2456-2378

Journal Content