A decade ago, two-parameter Burr Type X distribution was introduced by Surles and Padgett [14] which was described as Generalized Rayleigh Distribution (GRD). This skewed distribution can be used quiet effectively in modelling life time data. In this work, Bayesian estimation of the shape parameter of GRD was considered under the assumption of non-informative prior. The estimates were obtained under the squared error, Entropy and Precautionary loss functions. Extensive Monte Carlo simulations were carried out to compare the performances of the Bayes estimates with that of MLEs. It was observed that the estimate under the Entropy loss function is more stable than the estimates under squared error loss function, Precautionary loss function and MLEs.

In this paper, a new long term survival model called Nadarajah-Haghighi model for survival data with long term survivors was proposed. The model is used in fitting data where the population of interest is a mixture of individuals that are susceptible to the event of interest and individuals that are not susceptible to the event of interest. The statistical properties of the proposed model including quantile function, moments, mean and variance were provided. Maximum likelihood estimation procedure was used to estimate the parameters of the model assuming right censoring. Furthermore, Bayesian method of estimation was also employed in estimating the parameters of the model assuming right censoring. Simulations study was performed in order to ascertain the performances of the MLE estimators. Random samples of different sample sizes were generated from the model with some arbitrary values for the parameters for 5%, 1:3% and 1:5% cure fraction values. Bias, standard error and mean square error were used as discrimination criteria. Additionally, we compared the performance of the proposed model with some competing models. The results of the applications indicates that the proposed model is more efficient than the models compared with. Finally, we fitted some models considering type of treatment as a covariate. It was observed that the covariate  have effect on the shape parameter of the proposed model.

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In this article, an alternative method of defining the probability density function of Generalized Weibull-exponential distributions is proposed. Based on the method, the distribution can also be called Weibull exponentiated exponential distribution. This distribution includes the exponential, Weibull and exponentiated exponential distributions as special cases. Comprehensive mathematical treatment of the distribution is provided. The quantile function, mode, characteristic function, moment generating function among other mathematical properties of the distribution were derived. The parameters of the distribution were estimated by applying the Maximum Likelihood Procedure.The elements of the Fisher Information Matrix is also provided. Finally, a data set is fitted to the model and its sub-models. It is observed that the new distribution is more flexible and can be used quiet effectively in analysing real life data in place of exponential, Weibull and exponentiated exponential distributions.

Satellite imageries have in the recent past gained popularity in the areas of geo-informatics and geo-positioning because they provide global coverage and are cost-effective. Nevertheless, the use of these services poses questions on their spatial data quality in terms of positional reliability and accuracy, which have implications for their applicability. This study, therefore, analyzed the horizontal positional accuracy of satellite imageries (Google Earth and Bing) of Samaru in Kaduna state, Nigeria. The coordinates of 63 ground points (GPs) acquired with the Total Station instrument (Leica TCA 1201 M) were assessed against their corresponding points on the imageries using simple statistical accuracy metrics. The results revealed that the root mean square error (RMSE) of positions on the ground were significantly different from the RMSE of positions on the Google Earth and Bing imageries only in the Easting direction at the 95% significance level when p (2-tailed) = 0.000 [p < 0.05]. The study revealed that 50% and 70% of the Easting and Northing coordinates of the Google Earth imagery were related to the corresponding ground coordinates. In addition, 51% and 67% of the Easting and Northing coordinates of the Bing imagery were related to the corresponding ground coordinates. The results also showed that the Google Earth and Bing imageries had an overall positional accuracy of 6.09 m and 6.02 m, respectively, with the latter being more reliable in determining horizontal positions in the study area. The accuracy obtained was sufficient for navigation purposes and ground-based measurements that do not require very high accuracy. It was suggested, however, that a geometrical accuracy evaluation of similar or different imageries of the same study location or a more complex terrain should be undertaken to determine their reliability.