SOME APPLICATIONS OF EXPONENTIATED LOG-UNIFORM DISTRIBUTION

In this paper we introduced Exponentiated Log Uniform distribution as a generalisation of the Log Uniform distribution and its properties are studied. We provide graphical representations of its density function, cumulative distribution function, hazard rate function, and survival function. And derive various statistical properties such as moments, mean deviations, and quantile function of the new distribution. We also obtain the probability density functions of the order statistics of the Exponentiated Log-Uniform Distribution.To estimate the parameters of the distribution and the stress strength parameters, we use the maximum likelihood method, and validate the estimates of the model parameters through a simulation study. Our findings reveal that the Exponentiated Log-Uniform Distribution exhibits the least bias and that the values of the mean square error decrease as the sample size increases, indicating the effectiveness of this distribution in modeling real-world data. We applied the Exponentiated Log-Uniform distribution to a real data set and compared it with Exponentiated Quasi Akash Distribution and Exponentiated Weibull Distribution. It was found that the new distribution was a better fit than the other distributions based on the values of the AIC, CAIC, BIC, HQIC, the Kolmogorov-Smirnov (K-S) goodness-of-fit statistic and the p-values.