In this article, we introduce an extension referred to as the exponentiated Weibull power function distribution based on the exponentiated Weibull-G family of distributions. The proposed model serves as an extension of the two-parameter power function distribution as well as a generalization to the Weibull power function presented by Tahir et al. (2016 a). Various mathematical properties of the subject distribution are studied. General explicit expressions for the quantile function, expansion of density and distribution functions, moments, generating function, incomplete moments, conditional moments, residual life function, mean deviation, inequality measures, Rényi and q – entropies, probability weighted moments and order statistics are obtained. The estimation of the model parameters is discussed using maximum likelihood method. Finally, the practical importance of the proposed distribution is examined through three real data sets. It has been concluded that the new distribution works better than other competing models.
In this paper, we introduce a new family of univariate distributions with two extra positive parameters generated from inverse Weibull random variable called the inverse Weibull generated (IW-G) family. The new family provides a lot of new models as well as contains two new families as special cases. We explore four special models for the new family. Some mathematical properties of the new family including quantile function, ordinary and incomplete moments, probability weighted moments, Rѐnyi entropy and order statistics are derived. The estimation of the model parameters is performed via maximum likelihood method. Applications show that the new family of distributions can provide a better fit than several existing lifetime models.
The Topp-Leone distribution is an attractive model for life testing and reliability studies as it acquires a bathtub shaped hazard function. In this paper, we introduce a new family of distributions, depending on Topp–Leone random variable as a generator, called the Type II generalized Topp– Leone–G (TIIGTL-G) family. Its density function can be unimodel, leftskewed, right-skewed, and reversed-J shaped, and has increasing, decreasing, upside-down, J and reversed-J hazard rates. Some special models are presented. Some of its statistical properties are studied. Explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Rényi entropy and order statistics are derived. The method of maximum likelihood is used to estimate the model parameters. The importance of one special model; namely; the Type II generalized Topp–Leone exponential is illustrated through two real data sets.
In this article, we introduce a new class of five-parameter model called the Exponentiated Weibull Lomax arising from the Exponentiated Weibull generated family. The new class contains some existing distributions as well as some new models. Explicit expressions for its moments, distribution and density functions, moments of residual life function are derived. Furthermore, Rényi and q–entropies, probability weighted moments, and order statistics are obtained. Three suggested procedures of estimation, namely, the maximum likelihood, least squares and weigthed least squares are used to obtain the point estimators of the model parameters. Simulation study is performed to compare the performance of different estimates in terms of their relative biases and standard errors. In addition, an application to two real data sets demonstrate the usefulness of the new model comparing with some new models.
A new four-parameter lifetime distribution named as the power Lomax Poisson is introduced and studied. The subject distribution is obtained by combining the power Lomax and Poisson distributions. Structural properties of the power Lomax Poisson model are implemented. Estimation of the model parameters are performed using the maximum likelihood, least squares and weighted least squares techniques. An intensive simulation study is performed for evaluating the performance of different estimators based on their relative biases, standard errors and mean square errors. Eventually, the superiority of the new compounding distribution over some existing distribution is illustrated by means of two real data sets. The results showed the fact that, the suggested model can produce better fits than some well-known distributions.