A New Weibull-G Family of Distributions

Statistical analysis of lifetime data is an important topic in reliability engineering, biomedical and social sciences and others. We introduce a new generator based on the Weibull random variable called the new Weibull-G family. We study some of its mathematical properties. Its density function can be symmetrical, left-skewed, right-skewed, bathtub and reversed-J shaped, and has increasing, decreasing, bathtub, upside-down bathtub, J, reversed-J and S shaped hazard rates. Some special models are presented. We obtain explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Renyi entropy, order statistics and reliability. Three useful characterizations based on truncated moments are also proposed for the new family. The method of maximum likelihood is used to estimate the model parameters. We illustrate the importance of the family by means of two applications to real data sets

Power Generalized KM-Transformation for Non-Monotone Failure Rate Distribution

Lifetime models with a non-monotone hazard rate $\hspace{0.12cm}$ function have a wide range of applications in engineering and lifetime data analysis. There are different bathtub shaped failure rate models that are available in reliability literature. Kavya and Manoharan (2021) introduced a new transformation called KM-transformation which was found to be more useful in reliability and lifetime data analysis. Power generalization technique would be the best approach to deal with a system whose components are connected in series, in which the distribution of the component is KM-transformation of any lifetime model. In this article, we introduce a new lifetime model, Power Generalized KM-Transformation (PGKM) for Non-Monotone Failure Rate Distribution, which shows monotone and non-monotone behavior for the hazard rate function for different choices of values of parameters. We derive the moments, moment generating function, characteristic function, quantiles, entropy etc of the proposed distribution. Distributions of minimum and maximum are obtained. Estimation of parameters of the distribution is performed via maximum likelihood method. A simulation study is performed to validate the maximum likelihood estimator (MLE). Analysis of three sets of real data are given

A New Right-Skewed Upside Down Bathtub Shaped Heavy-tailed Distribution and its Applications

A one parameter right skewed, upside down bathtub type, heavy-tailed distribution is derived. Various statistical properties and maximum likelihood approaches for estimation purpose are studied. Five different real data sets with four different models are considered to illustrate the suitability of the proposed model