Reliability for Zeghdoudi distribution with an outlier, fuzzy reliability and application

Thara Belhamra; Halim Zeghdoudi; Vinoth Raman

doi:https://doi.org/10.59170/stattrans-2024-010

Reliability for Zeghdoudi distribution with an outlier, fuzzy reliability and application

Thara Belhamra Department of Mathematics, Science Faculty, Badji Mokhtar-Annaba University, 2300, Annaba, Algeria ORCID:https://orcid.org/0009-0008-4771-279X , Halim Zeghdoudi Department of Mathematics, Science Faculty, Badji Mokhtar-Annaba University, 2300, Annaba, Algeria ORCID:https://orcid.org/0000-0002-4759-5529 , Vinoth Raman Imam Abdulrahman Bin Faisal University Dammam, Eastern, Saudi Arabia ORCID:https://orcid.org/0000-0002-3815-2312 Statistics in Transition new series, vol. 25, 2024, 1, pages: 167-177 Published online: 6 March 2024 https://doi.org/10.59170/stattrans-2024-010 Citation: Belhamra, T., Zeghdoudi, H., Raman, V., 2024. Reliability for Zeghdoudi distribution with an outlier, fuzzy reliability and application. Statistics in Transition new series, 25(1), pp. 167-177. https://doi.org/10.59170/stattrans-2024-010.

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ABSTRACT

This study focuses on estimating reliability P[Y<X], where Y has a Zeghdoudi distribution with parameter a, X has a Zeghdoudi distribution with one outlier present and parameter c, and the remaining (n – 1) random variables are from a Zeghdoudi distribution with parameter b, in order for X and Y to be independent. Several findings of a simulation study and the maximum likelihood estimate of R are provided. We also present some results related to fuzzy dependability. Finally, using actual data on survival durations (in days) of 72 Algerians infected with a coronavirus, we demonstrate how the Zeghdoudi distribution may be applied to other distributions in order to demonstrate its adaptability.

KEYWORDS

Zeghdoudi distribution, maximum likelihood estimator, Newton-Raphson method, outlier, fuzzy reliability

REFERENCES

Bouhadjar M, Ahmed M. Gemeay, Ehab M. Almetwally, Zeghdoudi H, Etaf Alshawarbeh, Alanazi Talal Abdulrahman, M. M. Abd El-Raouf, and Eslam Hussam, (2022). The Power XLindley Distribution: Statistical Inference, Fuzzy Reliability, and COVID-19 Application. Hindawi Journal of Function Spaces, Vol. 2022, Article ID 9094078, 21 pages https://doi.org/10.1155/2022/9094078.

Deiri, E, (2010). Estimation of Reliability For Exponential Case In The Presence Of One Outlier. Financial Mathematics and Applications, Vol. 1, pp. 2217–7795.

Deiri, E., (2011). Estimation of P(Y < X) for Exponential Distribution in the Presence of Two Outliers. International Journal of Academic Research, Vol. 3, pp. 508–514.

Deiri, E., (2011). Estimation of P(Y < X) for Generalized Exponential Distribution in the Presence of Two Outliers when Scale Parameters is Known. International Journal of Academic Research, Vol. 3, pp. 1179–1185.

Deiri, E., (2011). Estimation of Parameters of the Gamma Distribution in the Presence of Two Outliers. International Journal of Academic Research, Vol. 3, pp. 846–852.

Dixit, U. J., M. Jabbari Nooghabi, M., (2011). Estimation of Parameters of Gamma Distribution in The Presence Of Outliers In Right Censored Samples. Aligarh Journal of Statistics, Vol. 31, pp. 17–29.

Dixit, U. J., (1989). Estimation of Parameters of the Gamma Distribution in the Presence of Outliers. Communications in Statistics – Theory and Methods, Vol. 18, pp. 3071–3085.

Dixit, U. J., Moor, K. L., and Barnett, V., (1996). On the Estimation of the Power of the Scale Parameter of the Exponential Distribution in the Presence of Outlier Generated from Uniform Distribution. Metron, Vol. 54, pp. 201–211.

Dixit, U. J., Nasiri, P. F., (2001). Estimation of Parameters of the Exponential Distribution with Presence of Outliers Generated from Uniform Distribution. Metron, Vol. 49(3–4), pp. 187–198.

Eslam Hossam, Alanazi Talal Abdulrahman, Ahmed M. Gemeay, Nawaf Alshammari, Etaf Alshawarbeh, Nour Khaled Mashaqbah, (2022). A novel extension of Gumbel distribution: Statistical inference with Covid-19 application. Alexandria Engineering Journal, Vol. 61, Issue 11, November 2022, pp. 8823–8842.

Fathy H. Riad, Bader Alruwaili, Ahmed M. Gemeay, Eslam Hussam, (2022). Statistical modeling for COVID-19 virus spread in Kingdom of Saudi Arabia and Netherlands. Alexandria Engineering Journal. Vol. 61, Issue 12, December 2022, pp. 9849–9866.

Jabbari Khamnei, H., Abolhasani, A., and Fathipour, P., (2012). Reliability for Six Parameter Generalized Burr XII Distribution with Transformation Method. Accepted in the Journal of Advances and Applications in Statistics.

Kapur, K. C., Lamberson, L. R., (1977). Reliability in engineering design. John Wiley and sons, New York.

Muqrin A. Almuqrin, Ahmed M. Gemeay, M. M. Abd El-Raouf, Mutua Kilai, Ramy Aldallal, and Eslam Hussam, (2022). A Flexible Extension of Reduced Kies Distribution: Properties, Inference, and Applications in Biology. Hindawi journal, ID 6078567, 19 pages https://doi.org/10.1155/2022/6078567.

Nasiri, P. F., Pazira, H., (2010). Bayesian and Non-Bayesian Estimations on the Generalized Exponential Distribution in the Presence of Outliers. Journal of Statistical Theory and Practice, Vol. 4(3), pp. 453–475.

Pak, A., Raqab M. Z., Mahmoudi, M. R., Band, S., Mosavi. A, (2022). Estimation of stress-strength reliability R = P(X > Y) based on Weibull record data in the presence of inter-record times. Alexandria Engineering Journal, Vol. 61, pp. 2130– 2144.

Ramy Aldallal, Ahmed M. Gemeay, Eslam Hussam, Mutua Kilai, (2022). Statistical modeling for COVID 19 infected patient’s data in Kingdom of Saudi Arabia, https://doi.org/10.1371/journal.pone.0276688.