On the New Weight Parameter of the Mixture Pareto Distribution and Its Application to Real Data

Chanaphun Chananet, Wikanda Phaphan

Abstract

This research aims to investigate the theoretical properties of new distribution which are based on the preceding well-known distributions by adding the new weight parameter. The new distribution is called the new weight parameter of the mixture of Pareto distribution. The advantage of the new distribution is the right-skewed distribution that is depending on the shape parameter. This property made the new mixture of Pareto distribution have high benefits of reliability engineering and survival analysis. Besides, we applied the purposed distribution to three sets of actual data: cement industry data, hard drive failure data, and heart attack data to show that new mixture Pareto distribution is fit to real data for generating data models.

Keywords

References

[1] H. W. Hager and L. J. Bain, “Inferential procedures for the generalized gamma distribution,” Journal of the American Statistical Association, vol. 65, no. 332, pp. 1601–1609, 1970.

[2] A. V. Boyd, “Fitting the truncated Pareto distribution to loss distributions,” Journal of the Staple Inn Actuarial Society, vol. 31, pp. 151–158, 1988.

[3] V. Brazauskas and S. Robert, “Favorable estimator for fitting Pareto models: A study using goodness-of-fit measures with actual data,” ASTIN Bulletin, vol. 33, no. 2, pp. 365–381, 2003.

[4] M. Doostparast and N. Balakrishnan, “Pareto analysis based on records, Statistics, vol. 47, no. 5, pp. 1075–1089, 2013.

[5] G. P. Patil and C. R. Rao, “Weighted distributions and size-biased sampling with applications to wildlife populations and human families,” Biometrics, vol. 34, no. 2, pp. 179–189, 1978.

[6] N. Nanuwong, W. Bodhisuwan, and C. Pudprommarat, “A new mixture Pareto distribution and its application,” Thailand Statistician, vol. 13, no. 2, pp. 191–207, 2015.

[7] J. A. Nelder and R. Mead, “A simplex method for function minimization,” The Computer Journal, vol. 7, no. 4, pp. 308–313, 1965.

[8] The R Development Core Team, R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing, 2018.

[9] Backblaze, “The Raw Hard Drive Test Data,” 2002. [Online]. Available: https://www.backblaze. com/b2/hard-drive-test-data.html

[10] R. Bhaskaran, “Echocardiogram-UCI,” 2018. [Online]. Available: https://www.kaggle.com/ loganalive/echocardiogram-uci

Full Text: PDF

DOI: 10.14416/j.asep.2020.10.002

Refbacks

There are currently no refbacks.

Username
Password
Remember me