The gamma-linear failure rate distribution: theory and applications

For any continuous baseline G distribution, Zografos and Balakrishnan [On families of beta- and generalized gamma-generated distributions and associated inference. Statist Methodol. 2009;6:344–362] introduced the generalized gamma-generated distribution with an extra positive parameter. A new three-parameter continuous model called the gamma-linear failure rate (LFR) distribution, which extends the LFR model, is proposed and studied. Various structural properties of the new distribution are derived, including some explicit expressions for ordinary and incomplete moments, generating function, probability-weighted moments, mean deviations and Rényi and Shannon entropies. We estimate the model parameters by maximum likelihood and obtain the observed information matrix. The new model is modified to cope with possible long-term survivors in lifetime data. We illustrate the usefulness of the proposed model by means of two applications to real data.     

Generalized exponential distributions

The three-parameter gamma and three-parameter Weibull distributions are commonly used for analysing any lifetime data or skewed data. Both distributions have several desirable properties, and nice physical interpretations. Because of the scale and shape parameters, both have quite a bit of flexibility for analysing different types of lifetime data. They have increasing as well as decreasing hazard rate depending on the shape parameter. Unfortunately both distributions also have certain drawbacks. This paper considers a three-parameter distribution which is a particular case of the exponentiated Weibull distribution originally proposed by Mudholkar, Srivastava & Freimer (1995) when the location parameter is not present. The study examines different properties of this model and observes that this family has some interesting features which are quite similar to those of the gamma family and the Weibull family, and certain distinct properties also. It appears this model can be used as an alternative to the gamma model or the Weibull model in many situations. One dataset is provided where the three-parameter generalized exponential distribution fits better than the three-parameter Weibull distribution or the three-parameter gamma distribution.     

The Conway–Maxwell–Poisson-generalized gamma regression model with long-term survivors

In this paper, we proposed a flexible cure rate survival model by assuming the number of competing causes of the event of interest following the Conway–Maxwell distribution and the time for the event to follow the generalized gamma distribution. This distribution can be used to model survival data when the hazard rate function is increasing, decreasing, bathtub and unimodal-shaped including some distributions commonly used in lifetime analysis as particular cases. Some appropriate matrices are derived in order to evaluate local influence on the estimates of the parameters by considering different perturbations, and some global influence measurements are also investigated. Finally, data set from the medical area is analysed.     

Best linear unbiased estimation of location and scale parameters of the log-logistic distribution

If an assumption, such as homoscedasticity, or some other aspect of an inference problem, such as the number of cases, is altered, our conclusions may change and different parts of the conclusions can be affected in different ways. Most diagnostic procedures measure the influence on one particular aspect of the conclusion - such as model fit or change in parameter estimates. The effect on all aspects of the conclusions can be described by the difference in two log likelihood functions and when the log likelihood functions come from an exponential family or are quasi-likelihoods, this difference can be factored into three terms: one depending only on the alteration, another depending only on the aspects of the conclusions to be considered, and a third term depending on both. The third term is interesting because it shows which aspects of the conclusions are relatively insensitive even to large alterations.     

Umvu estimation for certain family of exponential distributions

In this paper we study certain properties of estimable and UMUV-estimable functions in a subfamily of the one-parameter exponential family of distributions for which there exists a sufficient and complete statistic following a Gamma distribution. These results are applied to the problem of estimation in the transformed chi-square family.     

Mixture formulations of a bivariate negative binomial distribution with applications

This paper considers further mixture formulations of the bivariate negative binomial (BNB) distribution of Edwards and Gurland (1961) and Subrahmaniam (1966). These formulations and some known ones are applied (1) to obtain a bivariate generalized negative binomial (BGNB) distribution of Bhattacharya (1966), (2) to establish a connection between the accident-proneness models given by the BNB, BGNB and Bhattacharya's bivariate distributions, and (3) to compute the grade correlation and distribution function of the Wicksell-Kibble bivariate gamma distribution.     

Properties and applications of the sarmanov family of bivariate distributions

We discuss properties of the bivariate family of distributions introduced by Sarmanov (1966). It is shown that correlation coefficients of this family of distributions have wider range than those of the Farlie-Gumbel-Morgenstern distributins. Possible applications of this family of bivariate distributions as prior distributins in Bayesian inference are discussed. The density of the bivariate Sarmanov distributions with beta marginals can be expressed as a linear combination of products of independent beta densities. This pseudoconjugate property greatly reduces the complexity of posterior computations when this bivariate beta distribution is used as a prior. Multivariate extensions are derived.     

The cut-off point based on underlying distribution and cost function

Cut-off sampling has been widely used for business survey which has the right-skewed population with a long tail. Several methods are suggested to obtain the optimal cut-off point. The LH algorithm suggested by Lavallee and Hidiroglou [6] is commonly used to get the optimum boundaries by minimizing the total sample size with a given precision. In this paper, we suggest a new cut-off point determination method which minimizes a cost function. And that leads to reducing the size of take-all stratum. Also we investigate an optimal cut-off point using a typical parametric estimation method under the assumptions of underlying distributions. Small Monte-Carlo simulation studies are performed in order to compare the new cut-off point method to the LH algorithm. The Korea Transportation Origin – Destination data are used for real data analysis.     

A note on the multivariate generalized asymmetric Laplace motion

Abstract

In this note, we use multivariate subordination to introduce a multivariate extension of the generalized asymmetric Laplace motion. The class introduced provides a unified framework for several multivariate extensions of the popular variance gamma process. We also show that the associated time one distribution extends the multivariate generalized asymmetric Laplace distributions proposed in the statistical literature.     

Joint modeling of hierarchically clustered and overdispersed non‐gaussian continuous outcomes for comet assay data

Multivariate longitudinal or clustered data are commonly encountered in clinical trials and toxicological studies. Typically, there is no single standard endpoint to assess the toxicity or efficacy of the compound of interest, but co‐primary endpoints are available to assess the toxic effects or the working of the compound. Modeling the responses jointly is thus appealing to draw overall inferences using all responses and to capture the association among the responses. Non‐Gaussian outcomes are often modeled univariately using exponential family models. To accommodate both the overdispersion and hierarchical structure in the data, Molenberghs et al. A family of generalized linear models for repeated measures with normal and conjugate random effects. Statistical Science 2010; 25:325–347 proposed using two separate sets of random effects. This papers considers a model for multivariate data with hierarchically clustered and overdispersed non‐Gaussian data. Gamma random effect for the over‐dispersion and normal random effects for the clustering in the data are being used. The two outcomes are jointly analyzed by assuming that the normal random effects for both endpoints are correlated. The association structure between the response is analytically derived. The fit of the joint model to data from a so‐called comet assay are compared with the univariate analysis of the two outcomes. Copyright © 2012 John Wiley & Sons, Ltd.