Lomax-Cauchy{Uniform} Distribution: Properties and Application to Exceedances of Flood Peaks of Wheaton River

Abstract

In this article, we propose a new distribution called Lomax-Cauchy {Uniform} distribution (LCU) distribution using Cauchy distribution as the baseline distribution. Statistical properties such as mode, median, density of order
statistic, quantile fnction, skewness and kurtosis of the new Lomax-Cauchy {Uniform} distribution. We investigate the shapes of the density, hazard rate function, cummulative hazard function,linear representation of LCU distribution and asymptotic properties of the new Lomax-Cauchy {Uniform} distribution using simulation when n=20, 100, 500 and 1000. The measure of variation of uncertainty of random variable of LCUD is also determined. Maximum Likelihood estimation method is adopted in estimating the parameters. Lastly, the importance of the new LCU distribution is illustrated by comparing the proposed distribution with some existing distributions. The results show that the LCUD model provides consistently better fits than other competing models for the exceedances of flood peaks of Wheaton River data.