APPLICATIONS OF INVERSE WEIBULL RAYLEIGH DISTRIBUTION TO FAILURE RATES AND VINYL CHLORIDE DATA SETS

  • Aminu Adamu Ahmadu Bello University, Zaria
  • Abubakar Yahaya Ahmadu Bello University, Zaria
  • Hussaini Garba Dikko Ahmadu Bello University, Zaria
Keywords: Inverse Weibull-G family, Rayleigh distribution, Inverse Weibull Rayleigh distribution, Maximum likelihood estimation, Applications.

Abstract

In this work, a new three parameter distribution called the Inverse Weibull Rayleigh distribution is proposed. Some of its statistical properties were presented. The PDF plot of Inverse Weibull Rayleigh distribution showed that it is good for modeling positively skewed and symmetrical datasets. The plot of the hazard function showed that the proposed distribution can fit datasets with bathtub shape. Method of maximum likelihood estimation was employed to estimate the parameters of the distribution, the estimators of the parameters of Inverse Weibull Rayleigh distribution is asymptotically unbiased and asymptotically efficient from the result of the simulation carried out. Applying the new distribution to a positively skewed Vinyl Chloride data set shows that the distribution performs better than Rayleigh, Generalized Rayleigh, Weibull Rayleigh, Inverse Weibull, Inverse Weibull Weibull, Inverse Weibull Inverse Exponential and Inverse Weibull Pareto distribution in fitting the data as it has the smallest AIC value. Also, applying the new distribution to a negatively skewed bathtub shape failure rates data shows that the distribution is a competitive model after Weibull Rayleigh and Inverse Weibull Weibull distributions in fitting the data because it has the third least AIC value.

References

Amini, M., Mir Mostafaee, S., and Ahmadi, J. (2014). Log-gamma-generated families of distributions. Statistics, 48(4):913-932.
Ateeq, K., Qasim, T. B., and Alvi, A. R. (2019). An extension of Rayleigh distribution: Theory and applications. Cogent Mathematics & Statistics, (just-accepted):1622191.
Bhat, A. and Ahmad, S. (2020). A new generalization of Rayleigh distribution: Properties and applications. Pakistan Journal of Statistics, 36(3).
Chakrabarty, J. B. and Chowdhury, S. (2019). Compounded inverse weibull distributions: Properties, inference and applications. Communications in Statistics-Simulation and Computation, 48(7):2012-2033.
Cordeiro, G. M. and de Castro, M. (2011). A new family of generalized distributions. Journal of statistical computation and simulation, 81(7):883-898.
Elbatal, I., Ahmad, Z., Elgarhy, B., and Almarashi, A. (2018). A new alpha power transformed family of distributions: Properties and applications to the weibull model. Journal of Nonlinear Science and Applications, 12(1):1-20.
Eugene, N., Lee, C., and Famoye, F. (2002). Beta-normal distribution and its applications. Communications in Statistics-Theory and methods, 31(4):497-512.
Haq, M. and Elgarhy, M. (2018). The odd frechet-g family of probability distributions. Journal of Statistics Applications & Probability, 7(1):189-203.
Hassan, A. S. and Nassr, S. G. (2018). The inverse weibull generator of distributions: Properties and applications. Journal of Data Science, 16(4).
Khan, M. S., Pasha, G., and Pasha, A. H. (2008). Theoretical analysis of inverse weibull distribution. WSEAS Transactions on Mathematics, 7(2):30-38.
Kenny, J. and Keeping, E. (1962). Relative merits of mean, median and mode. Mathematics of Statistics, Van Nostrans NJ (ed), pages 211-212
Merovci, F. and Elbatal, I. (2015).Weibull rayleigh distribution: Theory and applications. Applied Mathematics & Information Sciences, 9 (4):2127.
Moors, J. (1988). A quantile alternative for kurtosis. Journal of the Royal Statistical Society: Series D (The Statistician), 37(1):25-32
Okasha, H. M., El-Baz, A., Tarabia, A., and Basheer, A. M. (2017). Extended inverse weibull distribution with reliability application. Journal of the Egyptian Mathematical Society, 25(3):343-349.
Tahir, M. H. and Cordeiro, G. M. (2016).Compounding of distributions: a survey and new generalized classes. Journal of Statistical Distributions and Applications, 3(1):1-35.
Published
2021-06-22
How to Cite
Aminu Adamu, Abubakar Yahaya, & Hussaini Garba Dikko. (2021). APPLICATIONS OF INVERSE WEIBULL RAYLEIGH DISTRIBUTION TO FAILURE RATES AND VINYL CHLORIDE DATA SETS. FUDMA JOURNAL OF SCIENCES, 5(2), 89 - 99. https://doi.org/10.33003/fjs-2021-0502-479