Properties and Applications of a Burr X-Lomax Distribution

Abstract

The properties of distribution functions, along with their interrelationships, are significant in the modeling of naturally occurring phenomena. This article proposed a new extension of the Lomax distribution by adding one shape parameter to the Lomax distribution using the Burr X-G family of distributions. This study has derived and investigated some statistical properties of the Burr X-Lomax distribution such as moments, moment generating function, the characteristics function, quantile function, survival function and hazard function. Some plots of the distribution and the reliability function were generated and interpreted appropriately. The model parameters have been estimated using the method of maximum likelihood estimation. The implications of the plots for the survival function indicate that the distribution (BuXLomD) can be used to model time or age-dependent events, where survival rate decreases with time or age. Also, the plots of the CDF and survival functions confirmed that the BuXLomD is a valid probability distribution. The performance of the Burr X-Lomax distribution has also been tested by application of the distribution to three real life datasets. Applications of the BuXLomD using three real life datasets revealed that the BuXLomD fits the dataset more appropriate and has better fitting performance than the transmuted Power Lomax distribution, Rayleigh-Lomax distribution, power Lomax distribution, sine Lomax distribution and the conventional Lomax distribution.