Kumaraswamy Inverse Lindley Distribution With Stress-Strength Reliability

Abstract

A new generalizing of inverse Lindley distribution called Kumaraswamy inverse Lindley is presented in this study. Some mathematical expressions are determined to the proposed distribution. Significant statistical measures are deduced including quantiles generating functions, ordinary and incomplete moments, entropies, mean deviations and order statistics. Some different properties such as, median, mean, variance, coefficient of variation, coefficients of skewness and kurtosis are characterized. Moreover, stress-strength reliabilities defined. Simulation study of the Kumaraswamy inverse distribution is introducedusing maximum likelihood estimation and the performances of their estimates are compered through biases and mean square errors. The applicability and importance of the new distribution is conducted through two real data groups.

Keywords

• Kumaraswamy inverse Lindley,Maximum likelihood

Kumaraswamy Inverse Lindley Distribution with Stress-Strength Reliability

Abstract

A new generalizing of inverse Lindley distribution called Kumaraswamy inverse Lindley is presented in this study. Some mathematical expressions are determined to the proposed distribution. Significant statistical measures are deduced including quantiles generating functions, ordinary and incomplete moments, entropies, mean deviations and order statistics. Some different properties such as, median, mean, variance, coefficient of variation, coefficients of skewness and kurtosis are characterized. Moreover, stress-strength reliabilities defined. Simulation study of the Kumaraswamy inverse distribution is introduced using maximum likelihood estimation and the performances of their estimates are compered through biases and mean square errors. The applicability and importance of the new distribution is conducted through two real data groups.

Keywords

• Kumaraswamy inverse Lindley,Stress-Strength reliability

References

1. [1] Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716-723.
2. [2] Al-Babtain, A., Fattah, A. A., Ahmed, A. H. N., and Merovci, F. (2017). The Kumaraswamy-transmuted exponentiated modified Weibull distribution. Communications in Statistics-Simulation and Computation, 46(5), 3812-3832.