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SYNOPTIC ABSTRACTThe modeling and analysis of lifetimes is an important aspect of statistical work in a wide variety of scientific and technological fields. We introduce and study the gamma-Nadarajah-Haghighi model, which can be interpreted as a truncated generalized gamma distribution (Stacy, 1962). It can have a constant, decreasing, increasing, upside-down bathtub or bathtub-shaped hazard rate function depending on the parameter values. We demonstrate that the new density function can be expressed as a mixture of exponentiated Nadarajah-Haghighi densities. Various of its structural properties are derived, including explicit expressions for the moments, quantile and generating functions, skewness, kurtosis, mean deviations, Bonferroni and Lorenz curves, probability weighted moments, and two types of entropy. We also investigate the order statistics. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is derived. We illustrate the flexibility of the new distribution by means of two applications to real datasets.

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The two-parameter Weibull has been the most popular distribution for modeling lifetime data. We propose a four-parameter gamma extended Weibull model, which generalizes the Weibull and extended Weibull distributions, among several other models. We obtain explicit expressions for the ordinary and incomplete moments, generating and quantile functions and mean deviations. We employ the method of maximum likelihood for estimating the model parameters. We propose a log-gamma extended Weibull regression model with censored data. The applicability of the new models is well justified by means of two real data sets.

Various applications in natural science require models more accurate than well-known distributions. In this context, several generators of distributions have been recently proposed. We introduce a new four-parameter extended normal (EN) distribution, which can provide better fits than the skew-normal and beta normal distributions as proved empirically in two applications to real data. We present Monte Carlo simulations to investigate the effectiveness of the EN distribution using the Kullback-Leibler divergence criterion. The classical regression model is not recommended for most practical applications because it oversimplifies real world problems. We propose an EN regression model and show its usefulness in practice by comparing with other regression models. We adopt maximum likelihood method for estimating the model parameters of both proposed distribution and regression model.