On a Novel Extended Lomax Distribution with Asymmetric Properties and Its Statistical Applications

In this article,we highlight a new three-parameter heavy-tailed lifetime distribution that aims to extend the modeling possibilities of the Lomax distribution.It is called the extended Lomax distribution.The considered distribution naturally appears as the distribution of a transformation of a random variable following the logweighted power distribution recently introduced for percentage or proportion data analysis purposes.As a result,its cumulative distribution has the same functional basis as that of the Lomax distribution,but with a novel special logarithmic term depending on several parameters.The modulation of this logarithmic term reveals new types of asymetrical shapes,implying a modeling horizon beyond that of the Lomax distribution.In the first part,we examine several of its mathematical properties,such as the shapes of the related probability and hazard rate functions;stochastic comparisons;manageable expansions for various moments;and quantile properties.In particular,based on the quantile functions,various actuarial measures are discussed.In the second part,the distribution’s applicability is investigated with the use of themaximumlikelihood estimationmethod.The behavior of the obtained parameter estimates is validated by a simulation work.Insurance claim data are analyzed.We show that the proposed distribution outperforms eight well-known distributions,including the Lomax distribution and several extended Lomax distributions.In addition,we demonstrate that it gives preferable inferences from these competitor distributions in terms of risk measures.

Flexible Reduced Logarithmic-Inverse Lomax Distribution with Application for Bladder Cancer

In this paper, a new method for adding parameters to a well-established distribution to obtain more flexible new families of distributions is applied to the inverse Lomax distribution (IFD). This method is known by the flexible reduced logarithmic-X family of distribution (FRL-X). The proposed distribution can be called a flexible reduced logarithmic-inverse Lomax distribution (FRL-IL). The statistical and reliability properties of the proposed models are studied including moments, order statistics, moment generating function, and quantile function. The estimation of the model parameters by maximum likelihood and the observed information matrix are also discussed. In order to assess the potential of the newly created distribution. The extended model is applied to real data and the results are given and compared to other models.

Acceptance Sampling Plans with Truncated Life Tests for the Length-Biased Weighted Lomax Distribution

In this paper,we considered the Length-biased weighted Lomax distribution and constructed new acceptance sampling plans(ASPs)where the life test is assumed to be truncated at a pre-assigned time.For the new suggested ASPs,the tables of the minimum samples sizes needed to assert a specific mean life of the test units are obtained.In addition,the values of the corresponding operating characteristic function and the associated producer’s risks are calculated.Analyses of two real data sets are presented to investigate the applicability of the proposed acceptance sampling plans;one data set contains the first failure of 20 small electric carts,and the other data set contains the failure times of the air conditioning system of an airplane.Comparisons are made between the proposed acceptance sampling plans and some existing acceptance sampling plans considered in this study based on the minimum sample sizes.It is observed that the samples sizes based on the proposed acceptance sampling plans are less than their competitors considered in this study.The suggested acceptance sampling plans are recommended for practitioners in the field.

A New Modified Inverse Lomax Distribution: Properties, Estimation and Applications to Engineering and Medical Data

In this paper,a modified form of the traditional inverse Lomax distribution is proposed and its characteristics are studied.The new distribution which called modified logarithmic transformed inverse Lomax distribution is generated by adding a new shape parameter based on logarithmic transformed method.It contains two shape and one scale parameters and has different shapes of probability density and hazard rate functions.The new shape parameter increases the flexibility of the statistical properties of the traditional inverse Lomax distribution including mean,variance,skewness and kurtosis.The moments,entropies,order statistics and other properties are discussed.Six methods of estimation are considered to estimate the distribution parameters.To compare the performance of the different estimators,a simulation study is performed.To show the flexibility and applicability of the proposed distribution two real data sets to engineering and medical fields are analyzed.The simulation results and real data analysis showed that the Anderson-Darling estimates have the smallest mean square errors among all other estimates.Also,the analysis of the real data sets showed that the traditional inverse Lomax distribution and some of its generalizations have shortcomings in modeling engineering and medical data.Our proposed distribution overcomes this shortage and provides a good fit which makes it a suitable choice to model such data sets.

Zubair Lomax Distribution:Properties and Estimation Based on Ranked Set Sampling

In this article,we offer a new adapted model with three parameters,called Zubair Lomax distribution.The new model can be very useful in analyzing and modeling real data and provides better fits than some others new models.Primary properties of the Zubair Lomax model are determined by moments,probability weighted moments,Renyi entropy,quantile function and stochastic ordering,among others.Maximum likelihood method is used to estimate the population parameters,owing to simple random sample and ranked set sampling schemes.The behavior of the maximum likelihood estimates for the model parameters is studied using Monte Carlo simulation.Criteria measures including biases,mean square errors and relative efficiencies are used to compare estimates.Regarding the simulation study,we observe that the estimates based on ranked set sampling are more efficient compared to the estimates based on simple random sample.The importance and flexibility of Zubair Lomax are validated empirically in modeling two types of lifetime data.

The Lambert-G Family:Properties,Inference,and Applications

This study proposes a new flexible family of distributions called the Lambert-G family.The Lambert family is very flexible and exhibits desirable properties.Its three-parameter special sub-models provide all significantmonotonic and non-monotonic failure rates.A special sub-model of the Lambert family called the Lambert-Lomax(LL)distribution is investigated.General expressions for the LL statistical properties are established.Characterizations of the LL distribution are addressed mathematically based on its hazard function.The estimation of the LL parameters is discussed using six estimation methods.The performance of this estimation method is explored through simulation experiments.The usefulness and flexibility of the LL distribution are demonstrated empirically using two real-life data sets.The LL model better fits the exponentiated Lomax,inverse power Lomax,Lomax-Rayleigh,power Lomax,and Lomax distributions.

On Modeling the Medical Care Insurance Data via a New Statistical Model

Proposing new statistical distributions which are more flexible than the existing distributions have become a recent trend in the practice of distribution theory.Actuaries often search for new and appropriate statistical models to address data related to financial and risk management problems.In the present study,an extension of the Lomax distribution is proposed via using the approach of the weighted T-X family of distributions.The mathematical properties along with the characterization of the new model via truncated moments are derived.The model parameters are estimated via a prominent approach called the maximum likelihood estimation method.A brief Monte Carlo simulation study to assess the performance of the model parameters is conducted.An application to medical care insurance data is provided to illustrate the potentials of the newly proposed extension of the Lomax distribution.The comparison of the proposed model is made with the(i)Two-parameter Lomax distribution,(ii)Three-parameter models called the half logistic Lomax and exponentiated Lomax distributions,and(iii)A four-parameter model called the Kumaraswamy Lomax distribution.The statistical analysis indicates that the proposed model performs better than the competitive models in analyzing data in financial and actuarial sciences.

Analysis and Optimum Plan for 3-Step Step-Stress Accelerated Life Tests with Lomax Model Under Progressive Type-I Censoring

Inthispaper,theoptimumtestplanandparameterestimationfor3-stepstep-stress accelerated life tests in the presence of modified progressive Type-I censoring are discussed.It is assumed that the lifetime of test units follows a Lomax distribution with log of characteristic life being quadratic function of stress level.The maximum likelihood and Bayesian method are used to obtain the point and interval estimators of the model parameters.The Bayes estimates are obtained using Markov chain Monte Carlo simulation based on Gibbs sampling.The optimum plan for 3-step step-stress test under modified progressive Type-I censoring is developed which minimizes the asymptotic variance of the maximum likelihood estimators of log of scale parameter at design stress.Finally,the numerical study with sensitivity analysis is presented to illustrate the proposed study.