Discrete Marshall–Olkin Lomax Distribution Application of COVID-19

In December 2019, Corona-Virus “COVID-19” was started in
Wuhan, China, On March 11, 2020, World Health Organization
(WHO) described COVID-19 as a pandemic...


Figure 2:
The situation for the daily new deaths over the world by the WHO Region.
In Lomax distribution: It is an important model for lifetime analysis, medical and business failure data, moreover it has been widely applied in a variety of contexts, it known as Lomax or Pareto type II distribution. Many authors have studied more applications by using extended Lomax distribution. [9] The question may come to mind of any researcher: why do we

Survival Discretization Method
In the statistics literature, sundry methods are available to obtain a discrete distribution from a continuous one. The most commonly used technique to generate discrete distribution is called a survival discretization method, it requires the existence of Cumulative Distribution Function (CDF), survival function should be continuous and non-negative and times are divided into unit intervals. The PMF of discrete distribution is defined in [11,12] as continuous distribution and Φ is a vector of parameters. The random variable X is said to have the discrete distribution if its CDF is given by The hazard rate is given by The reversed failure rate of discrete distribution is given as ( ) (

Discrete Marshall-Olkin Lomax Distribution
In this Section, we introduce a new flexible discrete model, can be donated as discrete Marshall-Olkin Lomax (DMOL) distribution.
Parameter estimation of DMOL distribution are discussed by using MLE.

The DMOL Distribution
The continues Marshall-Olkin Lomax (MOL) distribution is introduced by [9]. The survival function, of the MOL distribution, is given by Using the survival discretization method and survival function of MOL distribution, we define the PMF of the DMOL distribution as given below then 0 1, ρ < < the PMF can be rewritten as following  The CDF of the DMOL distribution is given as below x In The hr function of the DMOL distribution is given by Figure 5 shows the HRF plots of the DMOL distribution. It is noted that the shape of the HRF is increasing, left-skewed and decreasing.

Figure 5:
The HRF plots of the DMOL distribution.

Parameter Estimation
The unknown parameters of the DMOL distribution are obtained by the Maximum Likelihood Estimation (MLE) method. This method is based on the maximization of the log-likelihood for a given data set, assume that ( ) Hence, the likelihood equations are ( ) In The estimate of the parameter by using MLE, which can be obtained by a numerical analysis such as the Newton-Raphson algorithm.

Simulation Study
A simulation study is assumed to evaluate and compare the Simulated outcomes are listed in Tables 1 & 2 and the following observations are detected.
The bias and MSE decrease as sample sizes increase for all estimates (see Tables 1 & 2).  ρ γ

Concluding Remarks
In this article, with the aim of managing the risk of spreading These figures indicate that the DMOL distribution gets the lowest values of W*, A*, KS, and the largest P-value, among all fitted models.