Mathematical Statistics

Please cite this article in press as: Seke Etet PF, et al. Evaluation of the safety of conventional lighting replacement by artificial daylight. J Microsc Ultrastruct (2017), http://dx. a b s t r a c t Background: Short morning exposure to high illuminance visible electromagnetic radiations termed as artificial daylight is beneficial for the mental health of people living in geographical areas with important seasonal changes in daylight illuminance. However, the commercial success of high illuminance light sources has raised the question of the safety of long hour exposure. Methods: We have investigated the effect of the replacement of natural daylight by artificial daylight in Swiss mice raised under natural lighting conditions. Mice were monitored for neurotoxicity and general health changes. They were submitted to a battery of conventional tests for mood, motor and cognitive functions' assessment on exposure day (ED) 14 and ED20. Following sacrifice on ED21 due to marked signs of neurotoxicity, the expression of markers of inflammation and apoptosis was assessed in the entorhinal cortex and neurons were estimated in the hippocampal formation. Results: Signs of severe cognitive and motor impairments, mood disorders, and hepatotoxicity were observed in animals exposed to artificial daylight on ED20, unlike on ED14 and unlike groups exposed to natural daylight or conventional lighting. Activated microglia and astrocytes were observed in the entorhinal cortex, as well as dead and dying neurons. Neuronal counts revealed massive neuronal loss in the hippocampal formation. Conclusions: These results suggest that long hour exposure to high illuminance visible electromagnetic radiations induced severe alterations in brain function and general health in mice partly mediated by damages to the neocortex-entorhinal cortex-hippocampus axis. These findings raise caution over long hour use of high illuminance artificial light.

We introduce and study the Marshall-Olkin additive Weibull distribution in order to allow a wide variation in the shape of the hazard rate, including increasing, decreasing , bathtub and unimodal shapes. The new distribution generalizes at least eleven lifetime models extant in the literature. Various of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, moments of the residual and reversed residual life functions and order statistics are derived. The parameters of the new distribution are estimated by the maximum likelihood method. We illustrate empirically the superiority of the new model over other distributions by means of a real life data set.

This paper identifies the characteristics of three-parameter Burr Type XII distribution and discusses its utility in survivorship applications. It addresses the problem of estimating the three-parameter Burr XII distribution and its doubly truncated version. The results are applied on a real dataset by fitting the distribution to the survival time of breast cancer patients in the Gaza Strip. These data are known to have a heavy tailed distribution since patients in this area received different protocols of treatments in different levels of hospitals locally and abroad. The findings indicated that the estimates of the parameters of the truncated distribution are more efficient than those obtained from the original distribution since the distribution is heavy tailed and involves many highly extreme observations.

We investigate linear and nonlinear hypotheses testing in a Cox proportional hazards model for right-censored survival data when the covariates are subject to measurement errors. In Kukush and Chernova (2018) [Theor. Probability and Math. Statist. 96, 101-110], a consistent simultaneous estimator is introduced for the baseline hazard rate and the vector of regression parameters. Therein the baseline hazard rate belongs to an unbounded set of nonnegative Lipschitz functions, with fixed constant, and the vector of regression parameters belongs to a compact parameter set. Based on the estimator, we develop two procedures to test nonlinear and linear hypotheses about the vector of regression parameters: Wald-type and score-type tests. The latter is based on an unbiased estimating equation. The consistency of the tests is shown. Key words : Cox proportional hazards model, hypothesis testing, right censoring, simultaneous estimator of baseline hazard rate and regression parameter.

A new lifetime distribution is being introduced in this paper. The new distribution is quite flexible for analyzing positive data and has a bathtub-shaped hazard rate function. Some basic statistical functions associated with the proposed distribution are obtained. The parameters of the proposed distribution can be estimated by making use of the maximum likelihood approach. This distribution is fitted to model two lifetime data sets. The proposed distribution is shown to provide a better fit than related distributions as measured by two well-known goodness–of–fit statistics. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling positive data arising in various fields of scientific investigation such as the physical and biological sciences, reliability theory, hydrology, medicine, meteorology, survival analysis and engineering.

A generalization of the exponentiated Weibull geometric model called the transmuted exponentiated Weibull geometric distribution is proposed and studied. It includes as special cases at least ten models. Some of its structural properties including order statistics, explicit expressions for the ordinary and incomplete moments and generating function are derived. The estimation of the model parameters is performed by the maximum likelihood method. The use of the new lifetime distribution is illustrated with an example. We hope that the proposed distribution will serve as a good alternative to other models available in the literature for modeling positive real data in several areas.