Inference for the Birnbaum–Saunders Lifetime Regression Model with Applications

The Birnbaum–Saunders distribution is a positively skewed distribution that is frequently used for analyzing lifetime data. Regression analysis is widely used in this context when some covariates are involved in the life-test. In this article, we discuss the maximum likelihood estimation of the model parameters and associated inference. We discuss the likelihood-ratio tests for some hypotheses of interest as well as some interval estimation methods. A Monte Carlo simulation study is then carried out to examine the performance of the proposed estimators and the interval estimation methods. Finally, some numerical data analyses are done for illustrating all the inferential methods developed here.     

Estimation for one- and two-parameter exponential distributions under multiple type-II censoring

In this paper, we derive explicit best linear unbiased estimators for one- and two-parameter exponential distributions when the available sample is multiply Type-II censored. Further, after noting that the maximum likelihood estimators do not exist explicitly, we propose some linear estimators by approximating the likelihood equations appropriately. Some illustrative examples from life-testing experiments are also presented.     

Unusual presentation of a ring injury in a psychiatric patient

1. A ring embedded in the digits may result in erosion of the skin, tendons, and bones. 2. This type of injury may be prevented by removing the ring at the time of the injury. 3. All constricting bands should be carefully monitered and, if necessary, removed from fingers to prevent chronic erosion especially in people with a physical or mental disability.     

Effects of child mortality on subsequent fertility of women in some rural and semi-urban areas of certain Latin American countries

Abstract With the rapid decline in child mortality in developing countries there is considerable interest in understanding its effects on fertility. According to the theory of demographic transition, mortality declines are accompanied by fertility declines after a time lag, as countries go through the process of economic development. However, the immediate effects of a mortality decline on fertility have not been uniform as in many countries fertility has actually increased. For example, in many Latin American countries where mortality declines have been very rapid there have not been any appreciable changes in fertility. Only in recent years has there been a noticeable decline in the urban areas of some nations. While it is possible to examine the effects of various socio-economic factors on mortality and fertility at the macro-level, any real understanding of how mortality itself influences fertility would require information at the micro-level on couples who have experienced child mortality and who are also exposed to the risk of childbearing.     

Likelihood inference for lognormal data with left truncation and right censoring with an illustration

The lognormal distribution is quite commonly used as a lifetime distribution. Data arising from life-testing and reliability studies are often left truncated and right censored. Here, the EM algorithm is used to estimate the parameters of the lognormal model based on left truncated and right censored data. The maximization step of the algorithm is carried out by two alternative methods, with one involving approximation using Taylor series expansion (leading to approximate maximum likelihood estimate) and the other based on the EM gradient algorithm (Lange, 1995). These two methods are compared based on Monte Carlo simulations. The Fisher scoring method for obtaining the maximum likelihood estimates shows a problem of convergence under this setup, except when the truncation percentage is small. The asymptotic variance-covariance matrix of the MLEs is derived by using the missing information principle (Louis, 1982), and then the asymptotic confidence intervals for scale and shape parameters are obtained and compared with corresponding bootstrap confidence intervals. Finally, some numerical examples are given to illustrate all the methods of inference developed here.     

Correlates of caregiving burden in schizophrenia:A cross-sectional,comparative analysis from India

Schizophrenia is a global mental health issue that has serious implications not only for the person with the diagnosis, but for caregivers as well. In Asian societies, the family tends to be the “natural” caregiver in such situations and the caregiving function is usually shouldered by parents or the spouse. Asian communities tend to be more closely knit, and it would be expected that more social support would be available to those facing distressing circumstances such as managing the demands of a person with mental illness. This study seeks to explore the perceived burden in family caregivers of persons diagnosed with schizophrenia, the coping strategies that come into play, as well as the extent of social support available to them. Standardized instruments were administered to collect data at a teaching cum treatment facility in south India. A quantitative methodology was used to analyze cross-sectional data from 75 primary caregivers of people with a diagnosis of schizophrenia and a reference group of caregivers of patients with general medical ailments. Results indicate higher levels of burden, low social support, and poor coping in the caregivers of people with schizophrenia than the reference group. Implications for intervention with caregivers are also discussed in this article.     

Cubic rank transmuted distributions: inferential issues and applications

In this paper, we introduce a new family of transmuted distributions, the cubic rank transmutation map distribution. This new proposal increases the flexibility of the transmuted distributions enabling the modelling of more complex data such as ones possessing bimodal hazard rates. In order to illustrate the usefulness of the cubic rank transmutation map, we use two well-known lifetime distributions, namely the Weibull and log-logistic models. Several mathematical properties of these new distributions, namely the cubic rank transmuted Weibull distribution and the cubic rank transmuted log-logistic distribution, are derived. Then, the maximum likelihood estimation of the model parameters is described. A simulation study designed to assess the properties of this estimation procedure is then carried out. Finally, applications of the proposed models and their fit are illustrated with some datasets and the corresponding diagnostic analyses are also provided.     

On the hidden truncated bivariate Pareto (IV) model and associated inferential issues

Income and wealth data are typically modelled by some variant of the classical Pareto distribution. Often, in practice, the observed data are truncated with respect to some unobserved covariate. In this paper, a hidden truncation formulation of this scenario is proposed and analysed. For this purpose, a bivariate Pareto (IV) distribution is assumed for the variable of interest and the unobserved covariate. Some important distributional properties of the resulting model as well as associated inferential methods are studied. An example is used finally to illustrate the results developed here. In this case, it is noted that hidden truncation on the left does not result in any new model, but the hidden truncation on the right does. The properties and fit of such a model pose a challenging problem and that is what is focused here in this work.     

An EM type estimation procedure for the destructive exponentially weighted Poisson regression cure model under generalized gamma lifetime

In this paper, we assume the number of competing causes to follow an exponentially weighted Poisson distribution. By assuming the initial number of competing causes can undergo destruction and that the population of interest has a cure fraction, we develop the EM algorithm for the determination of the MLEs of the model parameters of such a general cure model. This model is more flexible than the promotion time cure model and also provides an interesting and realistic interpretation of the biological mechanism of the occurrence of an event of interest. Instead of assuming a particular parametric distribution for the lifetime, we assume the lifetime to belong to the wider class of generalized gamma distribution. This allows us to carry out a model discrimination to select a parsimonious lifetime distribution that provides the best fit to the data. Within the EM framework, a two-way profile likelihood approach is proposed to estimate the shape parameters. An extensive Monte Carlo simulation study is carried out to demonstrate the performance of the proposed estimation method. Model discrimination is carried out by means of the likelihood ratio test and information-based methods. Finally, a data on melanoma is analyzed for illustrative purpose.     

Inference for Type II bivariate Pólya–Aeppli distribution

In this article, we discuss the estimation of model parameters of the Type II bivariate Pólya–Aeppli distribution using the method of moments and the maximum likelihood method. We also compare some interval estimation methods. We then carry out a Monte Carlo simulation study to evaluate the performance of the proposed point and interval estimation methods. Finally, we present an example to illustrate all the inferential methods developed here.