The ArcTan Lomax Distribution with Properties and Applications

Authors

  • Arun Kumar Chaudhary  Department of Management Science (Statistics), Nepal Commerce Campus, Tribhuwan University, Kathmandu, Nepal
  • Vijay Kumar  Department of Mathematics and Statistics, DDU Gorakhpur University, Gorakhpur, Uttar Pradesh, India

DOI:

https://doi.org/10.32628/IJSRSET218117

Keywords:

ArcTan distribution, Estimation, Goodness-of-fit, Lomax distribution, MLE

Abstract

Here, in this paper, a continuous distribution called ArcTan Lomax distribution with three-parameter has been introduced along with some relevant properties of statistics and mathematics pertaining to the distribution. With the help of three established estimations methods including maximum likelihood estimation (MLE), estimation of the presented distribution’s model parameters is done. Also with the help of a real set of data, the distribution’s goodness-of-fit is examined in contrast to some established models in survival analysis.

References

  1. Chaudhary,A.K.& Kumar, V.(2020). The Logistic Lomax Distribution with Properties and Applications. International .International Journal of new technology and Research (IJNTR), 6(12), 74-80.
  2. El-Gohary, A., Alshamrani, A., & Al-Otaibi, A. N. (2013). The generalized Gompertz distribution. Applied Mathematical Modelling37(1-2), 13-24.
  3. Joshi, R.K. & Kumar, V. (2021). Poisson Inverted Lomax Distribution: Properties and Applications, International Journal of Research in Engineering and Science (IJRES), 9(1), 48-57. 
  4. Joshi, R.K. & Kumar, V. (2021). The Logistic Inverse Lomax Distribution with Properties and Applications, International Journal of Mathematics & Computer Research, 9(1) 2169-2177.
  5. Kleiber, C. (2004). Lorenz ordering of order statistics from log-Logistic and related distributions. Journal of Statistical Planning and Inference, 120, 13-19.
  6. Kleiber, C., & Kotz, S. (2003). Statistical size distributions in economics and actuarial sciences. John Wiley and Sons, Inc., Hoboken, New Jersey.
  7. Kumar, V. and Ligges, U. (2011). reliaR: A package for some probability distributions, http://cran.r-project.org/web/packages/reliaR/index.html.
  8. Kundu, D., and Raqab, M.Z. (2005). Generalized Rayleigh Distribution: Different Methods of Estimation, Computational Statistics and Data Analysis, 49, 187-200.
  9. Lemonte, A. J. (2013). 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.
  10. Lomax, K. S. (1954). Business failures: Another example of the analysis of failure data. Journal of the American Statistical Association49(268), 847-852.
  11. Mailund, T. (2017). Functional Programming in R: Advanced Statistical Programming for Data Science, Analysis and Finance. Apress, Aarhus N, Denmark ISBN-13 (pbk): 978-1-4842-2745-9 ISBN-13 (electronic): 978-1-4842-2746-6 DOI 10.1007/978-1-4842-2746-6
  12. Moors, J. (1988). A quantile alternative for kurtosis. The Statistician, 37, 25-32.
  13. Oguntunde, P. E., Balogun, O. S., Okagbue, H. I., & Bishop, S. A. (2015). The Weibull-exponential distribution: Its properties and applications. Journal of Applied Sciences15(11), 1305-1311.
  14. R Core Team (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
  15. Risti?, M. M., & Nadarajah, S. (2014). A new lifetime distribution. Journal of Statistical Computation and Simulation84(1), 135-150.
  16. Smith, R.M. and Bain, L.J. (1975). An exponential power life-test distribution, Communications in Statistics, 4, 469-481
  17. Swain, J. J., Venkatraman, S. & Wilson, J. R. (1988). Least-squares estimation of distribution functions in johnson’s translation system. Journal of Statistical Computation and Simulation, 29(4), 271–297.

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Published

2021-02-28

Issue

Section

Research Articles

How to Cite

[1]
Arun Kumar Chaudhary, Vijay Kumar "The ArcTan Lomax Distribution with Properties and Applications" International Journal of Scientific Research in Science, Engineering and Technology (IJSRSET), Print ISSN : 2395-1990, Online ISSN : 2394-4099, Volume 8, Issue 1, pp.117-125, January-February-2021. Available at doi : https://doi.org/10.32628/IJSRSET218117