The Transmuted Marshall-Olkin Extended Lomax Distribution.

A robust generalisation of the Gumbel distribution is proposed in this article. This family of distributions is based on the T-X paradigm. From a list of special distributions that have evolved as a result of this family, three separate models are also mentioned in this article. A linear combination of generalised exponential distributions can be used to characterise the density of a new family, which is critical in assessing some of the family's properties. The statistical features of this family are determined, including exact formulations for the quantile function, ordinary and incomplete moments, generating function, and order statistics. The model parameters are estimated using the maximum likelihood method. Further, one of the unique models has been systematically studied. Along with conventional skewness measures, MacGillivray skewness is also used to quantify the skewness measure. The new probability distribution also enables us to determine certain critical risk indicators, both numerically and graphically. We use a simulated assessment of the suggested distribution, as well as apply three real-world data sets in modelling the proposed model, in order to ensure its authenticity and superiority.

In this paper, a new three-parameter distribution called the Alpha Logarithm Transformed Fr\'{e}chet (ALTF) distribution is introduced which offers a more flexible distribution for modeling lifetime data. Various properties of the proposed distribution, including explicit expressions for the quantiles, moments, incomplete moments, conditional moments, moment generating function R\'{e}nyi and $\delta$-entropies, stochastic ordering, stress-strength reliability and order statistics are derived. The new distribution can have decreasing, reversed J-shaped and upside-down bathtub failure rate functions depending on its parameter values. The maximum likelihood method is used to estimate the distribution parameters. A simulation study is conducted to evaluate the performance of the maximum likelihood estimates. Finally, the proposed extended model is applied on real data sets and the results are given which illustrate the superior performance of the ALTF distribution compared to some other well-known distributions.

This paper proposes a new generator function based on the inverted Kumaraswamy distribution and introduces ‘generalized inverted Kumaraswamy-G’ family of distributions. We provide a comprehensive account of some of its mathematical properties that include the ordinary and incomplete moments, quantile and generating functions and order statistics. The infinite mixture representations for probability density and cumulative distribution and entropy functions of the new family are also established. The density function of the ith-order statistics is expressed as an infinite linear combination of baseline densities and model parameters are estimated by maximum likelihood method. Four special models of this family are also derived along with their respective hazard rate functions. The maximum likelihood estimation (MLE) method is used to obtain the model parameters. Monte Carlo simulation experiments are executed to assess the performance of the ML estimators under the corresponding generated models while some data applications are also illustrated. The results of the study show that the proposed distribution is more flexible as compared to the baseline model. This distribution especially can be used to model symmetric, left-skewed, right-skewed and reversed-J data sets.

For the first time, a four-parameter lifetime model, called the gamma extended Frchet distribution, is defined and studied.We obtain some of its mathematical properties.Explicit expressions for the ordinary and incomplete moments, quantile function, mean deviations, Rnyi entropy and reliability are provided.The order statistics and their moments are derived.The method of maximum likelihood is used for estimating the model parameters.We determine the observed information matrix.An application to a real data set shows that the new distribution can provide a better fit than other classical lifetime models.We hope that this generalization may attract wider applications in reliability, biology and survival analysis.

We propose a new family of continuous distributions called the odd generalized exponential family, whose hazard rate could be increasing, decreasing, J, reversed-J, bathtub and upside-down bathtub. It includes as a special case the widely known exponentiated-Weibull distribution. We present and discuss three special models in the family. Its density function can be expressed as a mixture of exponentiated densities based on the same baseline distribution. We derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves, Shannon and Renyi entropies and order statistics. For the first time, we obtain the generating function of the Frechet distribution. Two useful characterizations of the family are also proposed. The parameters of the new family are estimated by the method of maximum likelihood. Its usefulness is illustrated by means of two real lifetime data sets. AMS Subject Classification Primary 60E05; secondary 62N05; 62F10

We define and study a new generalization of the Fréchet distribution called the beta exponential Fréchet distribution. The new model includes thirty two special models. Some of its mathematical properties, including explicit expressions for the ordinary and incomplete moments, quantile and generating functions, mean residual life, mean inactivity time, order statistics and entropies are derived. The method of maximum likelihood is proposed to estimate the model parameters. A small simulation study is alsoreported. Two real data sets are applied to illustrate the flexibility of the proposed model compared with some nested and non-nested models.

In this article we introduce a new four - parameters model called the odd generalized exponential flexible Weibull extension (OGE-FWE) distribution which exhibits bathtub-shaped hazard rate. Some of it’s statistical properties are obtained including ordinary and incomplete moments, quantile and mode, the moment generating functions, reliability and order statistics. The method of maximum likelihood is used for estimating the model parameters and the observed Fisher’s information matrix is given. Moreover, we give the advantage of the OGE-FWE distribution by an application using real data.

A new lifetime model, which extends the Weibull distribution using the generalized transmuted-G family proposed by Nofal et al. (2016), called the generalized transmuted Weibull distribution is proposed and studied. Various of its structural properties including ordinary and incomplete moments, quantile and generating functions, probability weighted moments, ROnyi and q-entropies and order statistics are derived. The maximum likelihood method is used to estimate the model parameters. The new distribution is applied to two real data sets to illustrate its ‡exibility. It can serve as an alternative model to other lifetime models available in the literature for modeling positive real data in many areas.

ABSTRACTThis paper introduces a new four-parameter lifetime model called the Weibull Burr XII distribution. The new model has the advantage of being capable of modeling various shapes of aging and failure criteria. We derive some of its structural properties including ordinary and incomplete moments, quantile and generating functions, probability weighted moments, and order statistics. The new density function can be expressed as a linear mixture of Burr XII densities. We propose a log-linear regression model using a new distribution so-called the log-Weibull Burr XII distribution. The maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimation are discussed. We prove empirically the importance and flexibility of the new model in modeling various types of data.

We introduce a new class of distributions called the generalized odd generalized exponential family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, quantile and generating functions, R𝑒́nyi, Shannon and q-entropies, order statistics and probability weighted moments are derived. We also propose bivariate generalizations. We constructed a simple type Copula and intro-duced a useful stochastic property. The maximum likelihood method is used for estimating the model parameters. The importance and flexibility of the new family are illustrated by means of two applications to real data sets. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors via a simulation study.

This paper introduces a new lifetime distribution, the so-called odd log-logistic exponentiated Weibull distribution. The new distribution has the advantage of being capable of modeling various shapes of aging and failure criteria. We derive various of its structural properties including ordinary and incomplete moments, quantile and generating functions, and order statistics. The new density function can be expressed as a linear mixture of exponentiated Weibull densities. We propose a log-linear regression model using a new distribution, the log-odd log-logistic exponentiated Weibull distribution. The maximum-likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum-likelihood estimation are discussed. We prove empirically the importance and flexibility of the new model by modeling four real data sets.

This study introduces the Alpha Power Transformed Perks Distribution (APTPD), obtained by applying the alpha power transformation method to the classical Perks distribution in order to enhance its flexibility and enable it to accommodate different data structures. Several analytical properties of the proposed distribution are established, including a simplified expression for its probability density function, ordinary moments, moment-generating and characteristic functions, reliability measures, and order statistics. The parameter estimation for the APTPD is conducted using the method of maximum likelihood. To demonstrate its practical relevance, the APTPD is fitted to an engineering dataset on aircraft windshield service times and compared with several existing generalizations of the Perks distribution. Based on multiple goodness-of-fit statistics and information criteria, the APTPD provides the best fit among the considered competing models. Overall, the results indicate that the proposed distribution is a useful and flexible model for analyzing positively skewed lifetime data in reliability and survival studies.

We introduce a new four parameter continuous model, called the Kumaraswamy compound Rayleigh (KwCR) distribution that extends the compound Rayleigh distribution. We study some mathematical properties of this distribution such as; mean, variance, coefficient of variation, quantile function, median, ordinary and incomplete moments, skewness, kurtosis, moment and probability generating functions, reliability analysis, Lorenz, Bonferroni and Zenga curves, Rényi of entropy, order statistics and record statistics. We consider the methods of moments and maximum likelihood for estimating the model parameters.

In this paper, we consider transmuted generalized Lindley distribution, obtained via the quadratic rank transmutation map under the Lindley distribution. This distribution exhibits, in addition to decreasing, increasing and bathtub hazard rates, depending on its parameters, also unimodal hazard rate shape. A comprehensive mathematical treatment of this distribution is provided. Expressions for the moment generating function, moments, order statistics, residual life and reversed failure rate function are derived. The model parameters are estimated by the maximum likelihood method. A simulation study is performed to verify the behavior of the estimation procedure in terms of mean square errors and coverage probability. Global and local influence diagnostic procedures are provided. We then analyse a real data set on time-up-to-cure of patients treated with a triazole antifungal drug in an intensive care unit in Brazil.

A new generalization of the Frechet distribution called Lehmann Type II Frechet Poisson distribution is defined and studied. Various structural mathematical properties of the proposed model including ordinary moments, incomplete moments, generating functions, order statistics, Renyi entropy, stochastic ordering, Bonferroni and Lorenz curve, mean and median deviation, stress-strength parameter are investigated. The maximum likelihood method is used to estimate the model parameters. We examine the performance of the maximum likelihood method by means of a numerical simulation study. The new distribution is applied for modeling three real data sets to illustrate empirically its flexibility and tractability in modeling life time data.