The distribution of Pearson residuals in generalized linear models

In general, the distribution of residuals cannot be obtained explicitly. We give an asymptotic formula for the density of Pearson residuals in continuous generalized linear models corrected to order $n^{-1}$, where $n$ is the sample size. We define corrected Pearson residuals for these models that, to this order of approximation, have exactly the same distribution of the true Pearson residuals. Applications for important generalized linear models are provided and simulation results for a gamma model illustrate the usefulness of the corrected Pearson residuals

New Flexible Regression Models Generated by Gamma Random Variables with Censored Data

We propose and study a new log-gamma Weibull regression model. We obtain explicit expressions for the raw and incomplete moments, quantile and generating functions and mean deviations of the log-gamma Weibull distribution. We demonstrate that the new regression model can be applied to censored data since it represents a parametric family of models which includes as sub-models several widely-known regression models and therefore can be used more effectively in the analysis of survival data. We obtain the maximum likelihood estimates of the model parameters by considering censored data and evaluate local influence on the estimates of the parameters by taking different perturbation schemes. Some global-influence measurements are also investigated. Further, for different parameter settings, sample sizes and censoring percentages, various simulations are performed. In addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We demonstrate that our extended regression model is very useful to the analysis of real data and may give more realistic fits than other special regression models

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

The Kumaraswamy Marshal-Olkin Family of Distributions

We introduce a new family of continuous distributions called the Kumaraswamy Marshal-Olkin generalized family of distributions. We study some mathematical properties of this family. Its density function is symmetrical, left-skewed, right-skewed and reversed-J shaped, and has constant, increasing, decreasing, upside-down bathtub, bathtub and S-shaped hazard rate. We present some special models and investigate the asymptotics and shapes of the family. We derive a power series for the quantile function and obtain explicit expressions for the moments, generating function, mean deviations, two types of entropies and order statistics. Some useful characterizations of the family are also proposed. 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

Improved maximum likelihood estimators in a heteroskedastic errors-in-variables model

This paper develops a bias correction scheme for a multivariate heteroskedastic errors-in-variables model. The applicability of this model is justified in areas such as astrophysics, epidemiology and analytical chemistry, where the variables are subject to measurement errors and the variances vary with the observations. We conduct Monte Carlo simulations to investigate the performance of the corrected estimators. The numerical results show that the bias correction scheme yields nearly unbiased estimates. We also give an application to a real data set.Comment: 12 pages. Statistical Paper

Exposure to the complement C5b-9 complex sensitizes 661W photoreceptor cells to both apoptosis and necroptosis.

The loss of photoreceptors is the defining characteristic of many retinal degenerative diseases, but the mechanisms that regulate photoreceptor cell death are not fully understood. Here we have used the 661W cone photoreceptor cell line to ask whether exposure to the terminal complement complex C5b-9 induces cell death and/or modulates the sensitivity of these cells to other cellular stressors. 661W cone photoreceptors were exposed to complete normal human serum following antibody blockade of CD59. Apoptosis induction was assessed morphologically, by flow cytometry, and on western blotting by probing for cleaved PARP and activated caspase-3. Necroptosis was assessed by flow cytometry and Sirtuin 2 inhibition using 2-cyano-3-[5-(2,5-dichlorophenyl)-2-furyl]-N-5-quinolinylacrylamide (AGK2). The sensitivity of 661W cells to ionomycin, staurosporine, peroxide and chelerythrine was also investigated, with or without prior formation of C5b-9. 661W cells underwent apoptotic cell death following exposure to C5b-9, as judged by poly(ADP-ribose) polymerase 1 cleavage and activation of caspase-3. We also observed apoptotic cell death in response to staurosporine, but 661W cells were resistant to both ionomycin and peroxide. Interestingly, C5b-9 significantly increased 661W sensitivity to staurosporine-induced apoptosis and necroptosis. These studies show that low levels of C5b-9 on 661W cells can induce apoptosis, and that C5b-9 specifically sensitizes 661W cells to certain apoptotic and necroptotic pathways. Our observations provide new insight into the potential role of the complement system in photoreceptor loss, with implications for the molecular aetiology of retinal disease