Emp irica l mode ls to estimate the u ltraviolet index (UVI) for all sky conditions in ten locations in Upper Egypt have been developed. Multiple linear regression technique has been used for lin king each o f the UVI as a dependent variable, and all of the declination (δ), cosine solar zenith angle at noon (cosSZA n), total ozone column (TOC) in DU, reflectivity (reflc) in % and aerosol index (AI) as independent variables. A dataset corresponding to the period (1978-1999) was used to develop the models and an independent dataset (year 2000) was used for validation purposes. The data set for each location, including erythemal u ltraviolet (EUV) at noon in mW/ m 2 , (TOC) in DU, reflectiv ity (reflc) in % and (AI), was retrieved fro m Total Ozone Mapping Spectrometer (TOMS) remote sensing instrument. For all locations, the emp irical models exp lain more than 93% of UVI variab ility due to changes in all independent variables. In addit ion, one single model for all the locations has been constructed. Model performance was determined for each location by calcu lating the mean bias error (M BE %) and the root mean square error (RMSE %). In addition, mean absolute error (MAE %), modelling efficiency (M E), modelling index (d), and t-statistics have been computed. The empirical model provides reliable fo recast UVI in order to inform the public about the possible harmfu l effects of UV rad iation over-exposure.

By starting from the one-parameter Modified Borel-Tanner distribution proposed recently in the statistic literature, we introduce the zero-inflated Modified Borel-Tanner distribution. Additionally, on the basis of the proposed zero-inflated distribution, a novel zero-inflated regression model is proposed, which is quite simple and may be an interesting alternative to usual zero-inflated regression models for count data. The parameters of the proposed model are estimated by Maximum Likelihood Estimation technique. To check the potentiality of the zero inflated Modified Borel-Tanner regression, an application to the count of infected blood cells is taken. The results suggest that the new zero inflated Modified Borel-Tanner regression is more appropriate to model these count data than other familiar zero-inflated (or not) regression models commonly used in practice.

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