The Transmuted Weibull-Pareto Distribution

A new generalization of the Weibull-Pareto distribution called the transmuted Weibull-Pareto distribution is proposed and studied. Various mathematical properties of this distribution including ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves and order statistics are derived. The method of maximum likelihood is used for estimating the model parameters. The flexibility of the new lifetime model is illustrated by means of an application to a real data set

The Extended Burr XII Distribution with Variable Shapes for the Hazard Rate

<p>We define and study a new continuous distribution called the exponentiated Weibull Burr XII. Its density function can be expressed as a linear mixture of Burr XII. Its hazard rate is very flexibile in accomodating various shapes including constant, decreasing, increasing, J-shape, unimodal or bathtub shapes. Various of its structural properties are investigated including explicit expressions for the ordinary and incomplete moments, generating function, mean residual life, mean inactivity time and order statistics. We adopted the maximum likelihood method for estimating the model parameters. The flexibility of the new family is illustrated by means of a real data application.</p

A New Generalized Family of Distributions for Lifetime Data

A new class of continuous distributions called the generalized Burr X-G family is introduced. Some special models of the new family are provided. Some of its mathematical properties including explicit expressions for the quantile and generating functions, ordinary and incomplete moments, order statistics and Rényi entropy are derived. The maximum likelihood is used for estimating the model parameters. The flexibility of the generated family is illustrated by means of two applications to real data sets

The Marshall-Olkin Odd Burr III-G Family of Distributions: Theory, Estimation and Applications

We propose a new ‡exible class called the Marshall-Olkin odd Burr III family for generating continuous distributions and derive some of its statistical properties. We provide three special models which accommodate symmetrical, right-skewed and left-skewed shaped densities as well as bathtub, decreasing, increasing, upside-down bathtub and reversed-J shaped hazard rates. The model parameters are estimated by maximum likelihood, least squares and a percentile method. Some Monte Carlo simulations are performed to check the adequacy of these methods. The ‡exibility of a special model is illustrated by means of three applications to real data

The Extended Log-Logistic Distribution: Properties, Inference, and Applications in Medicine and Geology

In this paper, a new flexible extension of the log-logistic model called the extended odd Weibull log-logistic (EOWLL) distribution is studied. The EOWLL density can be expressed as a mixture of Dagum densities. The EOWLL distribution provides decreasing, increasing, upside-down bathtub, and reversed-J-shaped hazard rates, and right-skewed, symmetrical, and left-skewed densities. Its mathematical properties are derived. The EOWLL parameters are estimated via eight classical methods of estimation. Additionally, extensive simulations are obtained to explore the performance of the proposed methods for small and large samples. Two real-life sets of data from medicine and geology are analyzed, showing the flexibility of the EOWLL distribution as compared to other log-logistic extensions. The results show that the EOWLL distribution is more appropriate as compared to the Kumaraswamy transmuted log-logistic, alpha-power transformed log-logistic, and additive Weibull log-logistic distributions, among others

An Extended Burr XII Distribution: Properties, Inference and Applications

<p>We propose and study a new continuous model named the Marshall-Olkin exponentiated Burr XII (MOEBXII) distribution. It contains several special cases, namely the Marshall-Olkin exponentiated log-logistic, Marshall-Olkin exponentiated Lomax, Marshall-Olkin Burr XII, Marshall-Olkin log-logistic, Marshall-Olkin Lomax distributions, among others, and most importantly includes all four of the most common types of hazard function: monotonically increasing or decreasing, bathtub and arc-shaped hazard functions. Some of its structural properties are obtained such as the ordinary and incomplete moments, quantile and generating functions, order statistics and probability weighted moments. The maximum likelihood and least square methods are used to estimate the model parameters. A simulation study is performed to evaluate the precision of the estimates from both methods. The usefulness of the new model is illustrated by means of two real data sets.</p

A new inverse Weibull distribution: properties, classical and Bayesian estimation with applications

This article proposes a new extension of the inverse Weibull distribution called, loga- rithmic transformed inverse Weibull distribution which can provide better ts than some of its well-known extensions. The proposed distribution contains inverse Weibull, inverse Rayleigh, inverse exponential, logarithmic transformed inverse Rayleigh and logarithmic transformed inverse exponential distributions as special sub-models. Our main focus is to derive some of its mathematical properties along with the estimation of its unknown param- eters using frequentist and Bayesian estimation methods. We compare the performances of the proposed estimators using extensive numerical simulations for both small and large samples. The importance and potentiality of this distribution is analyzed via two real data sets

Inference on Constant Stress Accelerated Life Tests Under Exponentiated Exponential Distribution

Accelerated life tests have become increasingly important because of highercustomer expectations for better reliability, more complicated products withmore components, rapidly changing technologies advances, and the clear needfor rapid product development. Hence, accelerated life tests have been widelyused in manufacturing industries, particularly to obtain timely informationon the reliability. Maximum likelihood estimation is the starting point whenit comes to estimating the parameters of the model. In this paper, besides themethod of maximum likelihood, nine other frequentist estimation methodsare proposed to obtain the estimates of the exponentiated exponential distribution parameters under constant stress accelerated life testing. We considertwo parametric bootstrap confedence intervals based on different methods ofestimation. Furthermore, we use the different estimates to predict the shapeparameter and the reliability function of the distribution under the usualconditions. The performance of the ten proposed estimation methods isevaluated via an extensive simulation study. As an empirical illustration,the proposed estimation methods are applied to an accelerated life test dataset

Complete Study of an Original Power-Exponential Transformation Approach for Generalizing Probability Distributions

In this paper, we propose a flexible and general family of distributions based on an original power-exponential transformation approach. We call it the modified generalized-G (MGG) family. The elegance and significance of this family lie in the ability to modify the standard distributions by changing their functional forms without adding new parameters, by compounding two distributions, or by adding one or two shape parameters. The aim of this modification is to provide flexible shapes for the corresponding probability functions. In particular, the distributions of the MGG family can possess increasing, constant, decreasing, “unimodal”, or “bathtub-shaped“ hazard rate functions, which are ideal for fitting several real data sets encountered in applied fields. Some members of the MGG family are proposed for special distributions. Following that, the uniform distribution is chosen as a baseline distribution to yield the modified uniform (MU) distribution with the goal of efficiently modeling measures with bounded values. Some useful key properties of the MU distribution are determined. The estimation of the unknown parameters of the MU model is discussed using seven methods, and then, a simulation study is carried out to explore the performance of the estimates. The flexibility of this model is illustrated by the analysis of two real-life data sets. When compared to fair and well-known competitor models in contemporary literature, better-fitting results are obtained for the new model