ASYMMETRIC DOUBLE LOMAX DISTRIBUTION: THEORY AND APPLICATIONS

Asymmetric Double Lomax Distribution

In this paper, we introduce a new generalization of univariate and bivariate modified discrete Weibull distribution. Various properties of the univariate generalized modified discrete Weibull distribution, such as survival function, probability mass function, hazard rate function, probability generating function, and moment generating function, are derived. The joint distribution function, joint probability mass function, marginal distributions, moment generating function, and conditional distribution of the proposed bivariate distribution are derived. Parameters of the distributions are estimated using maximum likelihood estimation. The use of these distributions is illustrated using real-life datasets.

The double Lomax distribution is the ratio of two independent and identically distributed
classical Laplace distributions and it can be used to analyse data sets with heavy tails
and peakedness. In the present paper, we introduce asymmetric generalization of double
Lomax distribution. We derived the probability density function of asymmetric double
Lomax distribution and its various properties were studied. The maximum likelihood
estimation procedure is employed to estimate the parameters of the proposed distribution
and an algorithm in R package is developed to carry out the estimation. To validate the
algorithm, simulation studies were conducted with various parameter values. Finally, we
fitted the asymmetric double Lomax, asymmetric Laplace, double Lomax and Gaussian
distributions to microarray gene expression dataset and financial datasets and compared
them.