A Generalization of Lomax Distribution with Properties, Copula and Real Data Applications

Abstract

A new generalization of Lomax distribution is derived and studied. Some of its useful properties are derived. A simple clayton copula is used to generate many bivariate and multivariate type models. We performed graphical simulations to assess the finite sample behavior of the estimations. The new model is employed in modelling three real data sets.

The Double Burr Type XII Model: Censored and Uncensored Validation Using a New Nikulin-Rao-Robson Goodness-of-Fit Test with Bayesian and Non-Bayesian Estimation Methods

“…The 1 st data is the breaking stress data (see [29]). The 2 nd data presents survival times of guinea pigs see [30]. The 3 rd data are taxes revenue data see [20][21].…”

A New Probability Distribution for Modeling Failure and Service Times: Properties, Copulas and Various Estimation Methods

“…For more details see Elgohari and Yousof [25], Elgohari and Yousof [26], Al-babtain et al [3], Ali et al [4] and Ali et al [5].…”

A Novel Lomax Extension with Statistical Properties, Copulas, Different Estimation Methods and Applications

“…A special attention is paid to the Lomax distribution and its generalizations in applied statistics and related fields such as instance models, biological studies, wealth inequality, income, engineering, medicine, engineering, and reliability. The Lomax model is applied in modeling income and wealth data (see Harris [25] and Asgharzadeh and Valiollahi [10]), progressively type-II censored competing risks data [18], firm size data (see Corbellini et al [16]), engineering, reliability and economic data sets (see Elgohari and Yousof [19]), failure times data (see Chesneau and Yousof [15]), among others. Furthermore, many other Lomax extensions can be cited such as exponentiated Lomax [24], gamma Lomax [17], transmuted Topp-Leone Lomax [43], Kumaraswamy Lomax [32], Burr-Hatke Lomax [41], beta Lomax [32], odd loglogistic Lomax [19], Poisson Burr X generalized Lomax model [28], proportional reversed hazard rate Lomax [19], special generalized mixture Lomax [15], the Burr X exponentiated Lomax distribution and the Marshall-Olkin Lehmann Lomax distribution [2].…”

“…The Lomax model is applied in modeling income and wealth data (see Harris [25] and Asgharzadeh and Valiollahi [10]), progressively type-II censored competing risks data [18], firm size data (see Corbellini et al [16]), engineering, reliability and economic data sets (see Elgohari and Yousof [19]), failure times data (see Chesneau and Yousof [15]), among others. Furthermore, many other Lomax extensions can be cited such as exponentiated Lomax [24], gamma Lomax [17], transmuted Topp-Leone Lomax [43], Kumaraswamy Lomax [32], Burr-Hatke Lomax [41], beta Lomax [32], odd loglogistic Lomax [19], Poisson Burr X generalized Lomax model [28], proportional reversed hazard rate Lomax [19], special generalized mixture Lomax [15], the Burr X exponentiated Lomax distribution and the Marshall-Olkin Lehmann Lomax distribution [2]. However, other related Lomax models with different applications under censored and uncensored data can be found in Aboraya and Butt [3], Goual and Yousof [21], Ibrahim et al [27], Ibrahim [26] and Mansour et al [36].…”